(4x + 5)(x + 1) = 0, don’t make this HARD! (very easy to solve)

[@marywahoff7414]

Please ignore the negative comments, if they think they can do better, they should get their own channel, And stop criticizing this one. I am enjoying learning this again. This year I will be 65 years of age. Thank you for taking your time to bring this channel to us.

[@cpk805LM]

Agree. Of course you sound like a genius if you already know how to do them. I wonder how many could make those same comments if it was the first time they saw quadratics, which is obviously the audience he is targeting.

[@CasaErwin]

This one is easy, it's already factored. If the product is 0, then one of the factors must be 0. If 4x + 5 = 0, then x = -5/4. If x + 1 = 0, then x = -1. Now I'll watch the video to see if he gets it right. 🙂

[@twentyrothmans7308]

😀none of this expansion, then head-scratching for the formula.

[@sprky777]

Immediately see -1 as an obvious solution without algebra. A little more thinking to see the other possibility.

[@lachlan1971]

What I got.

[@juanrafaellattapiatarriaga9064]

For me is the same

[@Kualinar]

Did the same, after almost taking the long route.

[@richardlouis1284]

I hated math my entire life. Now retired I want to learn math and this channel has inspired me

[@michaelpurtell4741]

I don’t get it. The answer is given in the problem. How anyone make it difficult?

[@Marcuswelby-nx2te]

No you dont

[@user_wunderfackt]

Я тоже.

[@Mimibryant0123]

Me too

[@philippegingras]

Sorry for being so blunt, but I've watched a few of your videos now and I believe you are master at taking forever to get to the point

[@CasaErwin]

Thank you for saying that. You expressed it very well. In fact, sometimes it is very tedious to listen to the entire thing. I often turn it off after the answer is given and I can compare it to my own.

[@johnphilippeespiritusanto6124]

Impatient much?

[@voodooaudio9488]

He is used to charging by the hour, that's why.

[@robcampion9917]

Easy explanation: (4x+5) or (x+1) have to be 0 easiest solution 0-1=x so x=-1 , not even long enough for a KZbin short.

[@bigdog3628]

oh yeah I usually only watch his videos on my pc, so I can easily skip ahead. His longest video I can watch in a few minutes at most.

[@pattimyner3075]

Being almost 70 & have not been in class for a few years, ok maybe many years, I have enjoyed finding this. I always love math, and I like the way you explain every single thing. It makes sense then. I was looking at one of these last night when my son was here (he’s 50), and it became a talking point.

[@bobcarn]

I came up with two possible numbers for X: -1.25 or -1. I simply looked at it as if you're multiplying two numbers and come up with zero, one of those numbers must be 0. That would mean that one set of parentheses must work out to zero. That would make it either -1.25 for the left set, or -1 for the right set. I'm not sure though if that's the proper way of doing it, I'm not even sure what type of equation you'd call this, so now I'll watch the video. ... Yay! And I did learn a couple things about dealing with quadratic equations.

[@bugvswindshield]

i had -1 in about 10 seconds too. but that was because of the title only lol

[@flagmichael]

@@mroldnewbie It was the second solution, from the first term, that had to stand in line for our attention. The first one was just too easy to back off and look at both first.

[@bobettemorgan453]

I was traumatized with having two advanced math classes in the same day at college 8 yrs ago. How much had I retained? Glanced at this problem and solved it !!! Feel much better about my chances for handling dementia .

[@mclrose7]

I learned early on that when you move a number to the other side of the equal sign, you also switch the plus sign to negative or vice versa.

[@Danielle-nz9tn]

So interesting…I never heard of “moving a number to the other side of the equation” by “changing its sign” although I suppose it’s exactly what you’re doing. I only learned it conceptually as subtracting the items from the side of the equation with the variable, i.e. X, to help isolate the variable and then of course you have to subtract it from the other side (of course same applies for multiplying, adding, dividing, etc.-whatever is needed to get those numbers away from the variable X).

[@devonwilson5776]

Greetings. From the expression given, the values for X can be found by set 4X +5=0 and X+1=0. When 4X +5= 0, the value foe X = -5/4, and when X+1=0, the value for X will be negative 1.

[@AscDrew]

But logically, how can X have 2 different values? X=X , but -1 does Not = -5/4????

[@devonwilson5776]

@@AscDrew Greetings. X has two values because if you were to expand the expression you would turn up with a X^2 term in it. Therefore, X has two values that will satisfy the expression, either one should work. It is like saying X^2 =64. The values for X from this expression would be positive 8 and or negative 8 because (8×8)=64 and (-8×-8)= 64 also.

[@CasaErwin]

@@AscDrew Since this one has already been factored, you miss the big picture. This problem would normally be given as 4x^2 + 9x + 5 = 0, then, as part of solving the problem you would factor it into (4x + 5) (x + 1) = 0. One of these factors must be zero (that's the only way to get a zero product) so IF 4x + 5 = 0, then x = -5/4. IF x + 1 = 0, then x = -1. Either value (-5/4 or -1) when substituted back into the 4x^2 + 9x + 5 = 0 equation will give the correct result.

[@AscDrew]

I semi see what you are saying as I did what others wrote, but on a basic fundamental level the logic seems off that there can be two totally different answers to a math problem. Someone else explained it as two different points on a graph which seems to make more sense, but all seems odd. I haven’t done this kind of math in like 33 years, so pretty rusty.

[@MrGreensweightHist]

@@AscDrew Any number * 0 is 0. So if x is -1 (4x + 5)(x + 1) (4*-1+5)(-1+1) (-4+5)(0) -1*0 0 because the second () is 0 resulting in multiplying by 0 or -5/4 is -1.25 (4x + 5)(x + 1) (4*-1.25 + 5)(-1.25 + 1) (-5+5)(-1.25+1) 0*-0.25 0 because the first () is 0 resulting in multiplying by 0

[@shahrzadforouzanfard6499]

Thank you so much Mr. John Mathematics. I am 59 years old lady and Finally I got it with the simple formula PEMDAS that you have thought us. Thanks again.

[@poxyclypse]

I was not good at Algebra 2. Mostly, I kept dropping the negative during quadratics. But, I also didn't fully understand the zero-product property. My teacher was amazing, but I was sloppy. Though, when I got to Trig, I owned it. Thank you for this refresher!

[@CasaErwin]

It's really easy. If the product is zero, one of the factors must be zero.

[@jack002tuber]

Yes, taking trig will really sharpen your algebra skills. Worked for me

[@aleksa-77-7]

Please get to the solution, than explain all that other stuff. You are confusing me with all that extra talk before you solve anything.

[@orsonyancey4131]

Hi John, I just discovered your channel. I am age 68, a semi-retired engineer. I am having fun going back and studying high school mathematics from the famous Mary Dolciani books. By the way, your pace is fine, for teaching from scratch.

[@zachansen8293]

14:50 No. It can be zero if the left side is zero, both are zero **OR** only the right side is zero. You need to learn to be precise with your language. 15:11 -- see you changed it later to say that either can be zero.

[@robertjames5168]

He makes me hate math the way he explains it! So many variables, I cannot keep track, Thanks for making me feel dumb!

[@AXNJXN1]

Haven't been in math, minus one class around ten years ago, but 'this' kind of math was over 30 years ago... But, they way you teach it, I GOT THIS!!

[@jimlowry214]

He is a Teacher, anticipating the questions of neophytes. He is a good Teacher.

[@flyingspirit3549]

EXACTLY! Many will need, and benefit, for the longer, more detailed explanations. For those who can move faster, there is always the [skip ahead] key.

[@darkaether2798]

I probably cheated, but one of the values in brackets must be equal to zero. So on the right x= -1 and on the left x= -1.25 (or -5/4). Now I’ll watch the video!

[@WombatMan64]

That's exactly what I immediately thought. Will watch video now.

[@vaska1999]

The first idea is right, but x wil be -1 on the left as well. To get the result of 0, all you need is for the result of the right hand brackets to be 0 as anything multiplied by 0 is 0. (-4 + 5) = 1 x (-1 + 1) = 0, 1 x 0 =0.

[@WombatMan64]

@@vaska1999 that only gives you one of the two possible solutions though. x = -1.25 also returns 0

[@I_Love_Llamas]

I solved this using a theorem that states that if the product of two real numbers “a” and “b” is equal to zero, then at least one variable is equal to zero. In short, if ab = 0, then either one or both variables are equal to zero. So I simply solved the equations 4x + 5 = 0 and x + 1 = 0 respectively. 4x + 5 = 0 results in a solution of x = -5/4, and x + 1 = 0 results in a solution of x = -1.

[@randallthomas5207]

Do you remember the name of the theorem? I tutored while I was in college. What I discovered was that nearly all students could do the math. But were very confused with what rules to use when, and how. I started making them use simplified linear proofs so I could figure out where they went wrong. Started at the front of their book, and wrote every new theorem, law, or rule at the top of the page. Then below it they wrote five examples of it applied correctly in green. And a couple of examples below those in red ink. As they worked through homework problems they wrote the number of what the used to get to the new equation, then I knew what they were screwing up, and how. When they misused one of them, they wrote it down in red under that rule. I brought all of them up two grades.

[@pacmacdaddy]

Hi John! I was just reading through some of the comments and it’s a mixed bag mostly of appreciative but some are snarky and even snotty. By now you’ve grown a thick skin, otherwise you wouldn’t have lasted this long. When I was younger, in middle school and high school, I hated math-or at least I thought I did. My teachers always told me that if I just tried a little harder I would have gotten even higher grades. I remember just showing up in my math classes and not even putting in the effort to take notes like how the others did, but when it came to time for quizzes and exams, I still got a decent 80%-85%. But deep inside I had a love for math, and anything scientific. In retrospect, the main reason for my half-hearted effort was I was a jock, a football player that played first string running back, and played on all of the special teams. Long story short, when I got to college I began to immerse myself in my studies, and I fell in love with mathematics! So much so that I got into a competition with in my pre-calculus class with a whiz kid who seemed to get all of the problems solved! He and I battled as to who could get the most correct solutions with every test that our professor handed out, including who could get the most bonus problems solved! In the end it was split down the middle but in our final exam, Nguyen, got me because I made a mistake on a simple notation that I did not include in one of the bonus questions. I love your videos. I hope you continue to produce and publish them. The comments are just that, comments and opinions. Here’s my opinion. You are doing an unbelievable service to millions. Both of my parents were educators just like you. Educators take up their profession not because they will become wealthy. They choose it because they know that the forthcoming generations must have the tools to advance our evolution as a human race. For that, I am eternally grateful to you and the rest of your kind. Keep on doing what you’re doing, and we’ll keep wanting more. I am eternally grateful to you. ❤

[@pauline-q3p]

I had a wonderful math teacher. This bloke, honestly, no wonder so many have an aversion to learning math.

[@memyname1771]

(something)(something else)=0, therefore either (something) or (something else) must =0 If x+1 = 0 then x= -1 If 4x+5 = 0 then x= -5/4

[@woodstream6137]

My prealgebra teacher really prepped us to solve by factors. 15 second pop quiz: write all the primes from 1 to 100. 2 minute pop quiz: write all the numbers from 1 to 100 and their composites

[@m.h.6470]

Solution: the zero-product property says, that if "a * b = 0", that "a = 0" or "b = 0" or "a = b = 0". We can therefore split the given equation and say: 4x + 5 = 0 => x = -5/4 x + 1 = 0 => x = -1 Those are already all solutions of x.

[@robertgross578]

Very simple solution. Either term in parentheses equal to 0 will solve the equation. So 4x+5=0 and x+1=0 will solve the equations. The two solutions are x=-5/4 and x=-1.

[@thomasmaughan4798]

Simply adjust X such that the term in the parenthesis becomes zero. These are the roots of a quadratic equation. So X= (-1) is obviously one of the roots. 4x needs to equal -5, so x= -(5/4). Either value of X satisfies the equation.

[@KendyJane67]

This brings back memories! Enjoyed this video!

[@debrorahstuckey8857]

Same for me. That’s why I looked at these videos now!

[@joso5554]

AxB=0 is equivalent to (A=0 or B=0) So 2 solutions : 4X+5=0 which gives X=-5/4 X+1=0 which gives X=-1.

[@1234larry1]

I like this explanation because its possible that many algebra students solve quadratics mechanically without understanding why it works.

[@hughsonj]

Since the equation equals zero, you set each factor to equal zero. Then you solve for x in each factor, and you get two solutions: -5/4 or -1

[@ArthurAyala-n2j]

set the 2 factors equal = 0 4x+5=0 and x+1=0 and solve for x x=-5/4 and x=-1

[@gordysun]

Question (hope it makes sense): with the above solution, you assumed that both parts = i.e. (4x + 5) and (x + 1) both equal zero, but doesn't only one part need to equal 0, for (4x + 5)(x + 1) = 0 to be true? in other words, couldn't 4x + 5 equal a number, and x + 1 equal 0, so when multiplied together, the equation will end up 0 as shown? Keep up the great work by the way - love the channel!

[@thomasmaughan4798]

That is correct. This problem has TWO solutions also known as the "roots" of X. If it was graphed (=y rather than =0), it becomes a parabola and crosses X in two places; -1.25 and -1.

[@Serb4_Serb1]

backthen at school math used to be hard for me ... but when i have someone explain the foundation / the way of thinking / philosophy (n not doing it rushly) i can understand better n see math as fun.. tx u

[@michaelg.294]

I never took algebra, but it's obvious to me the answer is -1. I'm just surprised so many people commenting are trying to give 2 different values for X, saying the left X is this and the right X is that. I'm pretty sure X = X.

[@yodaami]

There are 2 solutions for this equation! Try putting -1 in and then putting -5/4. They aren’t saying the x s are different they are saying there are 2 solutions which will make the equation true! I’m guessing you’re well under 13 years old. You’ll get to it in later classes.

[@cs_fl5048]

HEY! I love the quadratic formula. I'm over 70, not a teacher, but I still know the QF. I just like math.

[@rondouglas5147]

I’m taking a SWAG on this on, it’s tricky, but my guess is -2.14, and I’m probably wrong. Now I’ll watch your solution. OK you came up with -5/4 = -1.25. Not sure where I screwed up, but will watch to fine my error. OK, just got to the 8 circle version and I’m I’m getting confused. Basically the way I remember it from 50 years ago is - (A1+ A2) * (B1 + B2) = 0, = A1*B1+ A1 * B2 + A2* B1 + A2*B2 = 0, solve for X. In my rush I may have made an error, but that’s basically it. Am I wrong? OK found my error. But at least you gave me a challenge this time.

[@darkst0rm2]

1:55 So anything times 0 is zero. So all the math here is simpler if you just solve x+1=0, which is -1

[@seadub1630]

I am guessing X= -1 as the second parentheses only needs to be zero to make it work. The first parentheses doesn't matter. Took less time than typing this. Now I'll go see if I am correct.

[@unclebrat]

This is a quadratic equation that has been factored. By the Fundamental Theorem of Algebra, there must be two roots. Now I will watch the video.

[@CasaErwin]

x = -1 is only half of the answer. When the product is zero, EITHER of the factors could be zero. The only thing we know for sure is that ONE of them has to be. So the complete answer is: If 4x + 5 = 0 then x = -5/4 and If x + 1 = 0, then x = -1.

[@williamlawrenson8345]

I think visual learners would appreciate drawing the parabola and highlighting what the solutions mean graphically.

[@valkrieknights]

I appreciate these videos because I haven't been in school in about 16 years. Helps refresh my knowledge. My first thought was obviously to do the FOIL method, but knew there was a simpler way. I essentially did the same thing as you but with extra steps. I divided both sides by the first binomial and solved. Then did the same with the second binomial and came to the same answers. Which is essentially what you did but since you knew the trick, you were able to skip a few steps.

[@chrisf5828]

I am not good at math but this took six seconds despite having forgotten what a quadratic equation is decades ago. Multiplying by zero equals zero so just make either of the multiplied values zero. So x=-1 or x=-1.25.

[@persephone342]

I believe the way they ask kids to “solve” the problems are at the root of why so many aren’t grasping math. Also, definitions are extremely important! Don’t allow his approach to disused you! Finding out exactly what that word means will be lock a brick that you’re laying in your fortress. You might forget it’s there, but just when you feel like that tower is going to collapse, you look back and realize that you fortified this tower with everything you needed. Mathematics is governed by a specific set of terminology.

[@irrefudiate]

I don't know algebra, but it occured to me that one of the parenthesis had to be zero and the easiest way to do that was to make X = -1.

[@littlegems5097]

Yup, that's the easy way he was talking about well done, and I know you mean the second parenthesis.

[@CasaErwin]

Correct. But we don't get to choose which one. A quadratic equation always has two solutions.

[@MrGreensweightHist]

@@CasaErwin not always

[@AntoniusReginaldus]

That's essentially what I did, in my head. I wanted to justify the result of 0 and when I saw multiplication happening, I wanted to make it so that I could create a 0 and the second parentheses made that easy; from there, it didn't matter what was going on in the first parenthesis, since I would get 0 when multiplying by 0. So I was able to get one of the correct possibilities. I can easily speculate that this would be a lot harder when 0 is not the result, because I wouldn't be able to rely upon that simple rule to find my answer. In which case I would have to rely on this longer stuff he showed.

[@jeffwells641]

​@MrGreensweightHist Yes always. You're thinking of the step before getting to the quadratic equation. If in setting up the quadratic equation you multiply the equation by a variable, then one of the solutions to the quadratic equation may not correctly solve the originating equation. This is called an extraneous solution, and is discarded. But only after you've gotten two solutions to the quadratic equation, and then proved that one is extraneous. You ALWAYS get two solutions to the quadratic equation, but occasionally only one of the solutions is the ultimate answer your looking for. When you get out of pure math problems and get into more practical real life problems it hairballs much more frequently that only one answer to a quadratic equation (one answer may put you below ground, for example, and it's therefore not what you're looking for).

[@thomasmathew257]

It is very easy to solve. Either (4x+5) =0 giving x=-5/4or (x+1) =0 giving x=-1. So -5/4 and -1 are the solutions.

[@wimharter]

The quadratic formula is the best way. The numbers can put into calculator or spreadsheet.

[@krunoslavregvar477]

x1= - 5/4 x2 = - 1

[@orvilledyer9904]

You explain it perfectly. Great teacher

[@alcoholfree6381]

I got it again! I merely used a few tricks which I’ve seen on your other videos. I haven’t done problems like these since High School, over 53 years ago. It’s fun to see how easy it is to solve these problems with simple techniques; taught by you. Keep up your great work!

[@mr.mxyzptlks8391]

1st level of abstraction. a*b=0.a or b has to be zero. So you end up with 2 linear equations to solve. In this case multiplying out and solving the quadratic should work out fine, but, there is an underlying principal that expands this concept way further. Go on to university and find out what that is 😎

[@Katy02u2]

I enjoyed math in school. I can recall that math was presented from easy, building to more complicated. Do you have such a system?

[@xlerb2286]

Watching this video I realize just how much I've forgotten since high school and university. I was in comp sci so there was plenty of math and I was good at it. Straight A's in all math classes and I even had a few 100%'s on midterms and finals. But I haven't much used it in the 40 years since. I still remember enough to know at a glance how to solve this the easy way. But listening to the rest of the video involved me saying "oh that's right" and "I'd forgotten that" than I'd have liked ;)

[@janicefisher.8215]

Thank you for reminding me about the zero property. I used foil to begin with. 😊

[@vaska1999]

The result on either of the brackets must be 0 so as to yield the final result of 0. -1 + 1 = 0. (-4 +5) x (-1 + 1) = 1 x 0 = 0.

[@billmorgan5327]

No, quadratic equations DO NOT always have 2 solutions as you stated. You can have 0, 1 or 2 solutions depending on the quadratic equation, since you didn't want to talk about imaginary/complex numbers.

[@thomasmaughan4798]

correct; and cubic expressions can have zero, 1 2 or 3 roots (and so on).

[@pcatful]

My algebra teacher would not have said I was an expert in anything! But this was easy for me (though I wasn't totally sure).

[@twinlions8955]

My teacher rarely spoke, she did the algorithm on the board step by step and we all got it!

[@volvol1]

The answer is -1. Anything times zero is zero.

[@millville]

I'm a bit disappointed you didn't also show how to proceed from 4X²+9X+5=0. I would do 4x²+9X = -5, then divide both sides by X to get 4X+9 = -5/X. Then move X's left again and the nine to the right: 4X + 5/X = - 9 . THEN let X= -1 (just for fun) and I get -4-5 = -9 (-9 = -9) which is TRUE!!!!!!! How would you have done it?

[@andtrrrot]

What's the 2nd solution?

[@TheAnimeist]

@millville 100% this question. How would you solve it the 4X²+9X+5=0 way? Refactor first the equation to (4x+5)(x+1)=0?

[@WombatMan64]

@@TheAnimeist If you've got any formula of the form ax² + bx + c = 0 (where a, b, and c are any real number) then yeah, the easiest way is factor if you can, but that's not always easy to do. You can derive the formula to solve for x (which I remember doing in high school) but for the sake of ease here it it: x = -b ± √(b²-4ac) / 2a

[@TheAnimeist]

@@WombatMan64 My word. I fee like an idiot. Highschool was so long ago. Thanks for revealing the answer. 🛹😎

[@CasaErwin]

@@TheAnimeist Exactly

[@HuxtableTV]

You are the best math teacher !

[@Cam-SB]

Thank you for teaching math on KZbin. I know someone whose kid would just type in google his math equations for the answers; because google will give you the answer WITH a step by step explanation of how to get there. Atleast this video isn't giving every equation's answer, so there is no cheating.

[@jonathansmith336]

You can end with one solution if the vertex is on the x-axis though technically it is counted twice. Better explain that if you're going to say there will always be TWO solutions or you will have to deal with it later.

[@asphaltandtacos]

I knew exactly what the answers would be. The problem was in simple form from the start so only basic math operations were needed.

[@joemasters2270]

x= -1. 4x = -4. -4 + 5 = 1. -1 +1 = 0. Any number multiplied by 0 is 0.

[@flagmichael]

It took less than five seconds and little more than a glance. The second term, (x+1), had to be zero or in the first term x+5/4 had to be zero. The two solutions are x=-1 and x=-5/4.

[@dalphonhamilton9980]

This one is easy as long as you remember that a real number times 0=0. So set 4X+5=0 and/or X+2=0. Therefore X= -5/5 and X=-1

[@shannonmcdonald7584]

Each factor set equal to zero, one result is extraneous, one answer is correct. 5/4 is extraneous

[@w.j.d.m]

Good, but taking a lot of time to start, please be a bit, quicker to hit the nail right at the top, and that's why some of us hatred this subject.

[@fredogden936]

You pretty much described me at the end of the video. After 45 years, I still struggle with algebra. Geometry, no problem. The trigonometry I took was no problem. But algebra has always busted my chops.

[@AuttumnDawn]

I'm the same. However I had a great Algebra 1 teacher. Who would make everything make sense. Like you are having a party. X amount of people were invited. Y RSVP. How much food should you make because z will show up without RSVPing. All of a sudden you're like, ohhhh I get it now. However with my Dsyliex brain, I never understand show your work. Me the answer is -1. How did you get there. Me using very simple math. Teacher No, it's takes the long route. Me so the answer is still -1. That's what I got.

[@stevie3011]

-1 because -1 + 1 = 0, or -1.25 because (-1.25 * 4) + 5 is also 0

[@aidanmargarson8910]

i just did it in my head .. -b plus or minus the square root of b^2 - 4ac over 2A

[@StephanBuchin]

So simple and so clearly explained. I wish I hadn't already forgotten everything in a week 😐

[@JesusChrist-xb7jq]

I gave up waiting for the answer, but I know that everything in the parentheses equals a number. (Number) x (number) = 0. Anything x 0 = 0. And the easiest one to solve is the second (number). -1 + 1 = 0. X = -1 Plug answer for x into the first (number). 4 x -1 = -4 -4 x 5 = -20 -20 x 0 = 0 If I tried, maybe I could figure out how he got the second answer. But in my mind, having just one is good enough 😂.

[@doreencloutier1066]

Do the same thing to each side of the equation. -5 from both sides. 4x=-5. Then divide both sides by 4 to get x. X=-5/4

[@dzadza7775]

Very nice friendly approach. Takes his time which can only be helpful. Thank you.

[@lukeknowles5700]

one of the two numbers must always be 0 if multiplying two numbers yields 0. This is because the multiplication property of zero states that the product of any number and zero is zero.

[@AnthonyWhitehorne-y1l]

Hey, mot everyone is as bright as you. The man is making it easier for those who are slower. Please be patient and remember that others may benefit from his slowness. That's the mark of a good teacher.

[@ChristinaEbuang]

Thank you, math-man. This your channel is for people like me who need to understand because I know very little about mathematics but want to learn more.

[@flagmichael]

This is a refreshing change from his reliance on PEMDAS, which I regard as a threat to certainty. This one does not rely on a magic decoder ring, just good old basic algebra.

[@JohnGriffith-w2w]

Okay! Students remember! You do have to graduate from High School 🏫! So do learn and remember this nonsense well enough to graduate however, when you finish with school it is far more important and valuable to have learned how to show up on time with a good attitude consistently than ANY of the jibberish in this post! Enjoy your paycheck!

[@izzzzzz6]

I'm confused. How can there be two different answers? If i put -5/4 into my calculator i get -1.25 but by looking at the equation i guessed -1 last time i checked -1 and -1.25 are not the same.

[@Danielle-nz9tn]

I think it has to do with the equation resulting in a parabola, where there are two values that work in the equation to make zero (one of them is in the quadrant of the graph above zero and the other is in the quadrant below zero. My algebra is super rusty, but I think this is correct. Maybe someone can verify or expand on my answer?

[@hawk1481]

I think I’m gonna look up your basic fraction courses and start there

[@kimobrien.]

You have two factors whose product is zero. One or both factors must therefore be equal to zero.

[@deputy1968]

Another great problem. Thank you!

[@stacyroe619]

Love your content, though I've only seen two of your videos so far. I just love math and science in general. this equation was ridiculously simple because of the fact that the result was zero and the last step was multiplication. it meant that one of the two or both of brackets had to have a result of 0. so I assumed a 50-50 shot that x + 1 was 0 making x - 1 and when I tried to do the same thing for 4x + 5 I found out it got complicated quickly and I decided to go with k.i.s.s. theory. I could have found a solution but I already had one and I figured screw it I'd just watch your video. had the result of the equation been anything at all whatsoever other than zero the equation would have been a lot more challenging but then I've always been one to resolve things by exceedingly unorthodox methods. when I was a kid a few hours after learning how to count I was doing addition subtraction multiplication and division because my mother taught me it was all just counting as a result I went into kindergarten doing math several grades above my status and I've always done math the wrong way ever since. it makes it harder takes longer but it means I don't always need to understand the equation to get the right answer. Though eventually I did have to learn how to do it the right way because some equations are too complicated to do in one lifetime any other way.

[@MR-go8wn]

Very easy. Thank you.

[@BobbyJardine-vs8yc]

I put these equations into Wolfram app and it explains it and doesn't over talk.This guy puts you to sleep by beating around the bush.He keeps on repeating the same thing over and over and never gets to the point.Ill bet his students keep switching teachers.

[@TheBossDroid]

Awesome teacher!

[@joejoe-lb6bw]

Should be emphasized that this is true for quadratic equations. Would this shortcut work for cubics?

[@lilianaprina5991]

Thanks, you forgotten to include the formula for other cases of quadratics...

[@JohnHughesChampigny]

If A times B is zero then either A or B is zero. So either 4x + 5 = 0 or x + 1 = 0, so either x = -5/4 or x = -1. Simples.

[@RaymondMartin-z1h]

I would just divide both sides by (4x+5) first. Then solve for X

[@nicoleb3636]

Been a while, but when you say "easy way," reminds me for the whole equation to be zero, either x+1 or 4x+5 has to be zero meaning x is -1 or x is -5/4.

[@AscDrew]

But how can x be two different numbers?

[@nicoleb3636]

@AscDrew If you think of this as a function, you have (4x+5)(x+1)=y. To "solve" for x, you find the value of x when the function (y) equals 0 (meaning it intersects/crosses the x axis). If you were to graph this function, you would see a parabola. That parabola will intersect the x axis at two points (-1,0) and (-5/4, 0). These are the two solutions for x (when x=-1 and x=-5/4). Note that you only plug in one value for x into the function at a time. When x is -1, the function says (-4+5)(-1+1)=0 which is true. When x is -5/4, the funtion says (-20/4 + 5)(-5/4 +1)=0 which is true. Two more (x,y) points on the graph are (-1/2, 3/2) and (-3/2, 1/2). These are NOT "solutions" for x, because y is not 0 (not intersecting x axis at that point), but they are two more points if you were to go on to graph this parabola on paper. On the other hand, a linear equation like x-10=y makes a straight line, so it intersects the x axis at one point when x-10=0 so x has one solution (x=10).

[@rgrinnell]

X= -1

[@annamelendrez8929]

Love the videos. Review classes for me. Thanks.

[@CybeleCotter]

The simplest way of solving is to make either parenthesized value zero, as anything times zero equals zero.

[@Danielle-nz9tn]

I’m thinking that x = -1 or x = 1 1/4 because that would make either one of the expressions in parentheses equal zero, making the equation equal to zero.

[@bigdog3628]

I never thought of it that way, I was always taught the vortex method or the quadratic formula. (IE, you gotta take the long way lol)

[@jackmckinnon8073]

I got it right but couldn't remember what the type of equation was or what its solution was called.

[@markmccullough5873]

Two solutions. X=-1, X=-1.25

[@chrisharris1522]

0 x anything =0 all you need to do is make one of the factors = 0 no pencil required here

[@sporkstar1911]

Fast Take - what I see myself doing here is dividing both sides by the first parentheses... so X+1 = 0/(4x+5). Scotty... beam me up, because I think that means X is -1, due to -1+1 = 0. It wouldn't matter what was in the divisor as long as it wasn't a div0.

[@The3dgerin]

Hmm I am terrible at math but I did this one in my head, x=0 so the only way you could get 0 is when your doing the parenthesis one of them had to be zero in order to have x=0. The logical choice was the second group of x+1. In order to get that to be zero x had to be -1+1=0. The first group was irrelevent because whatever number it totaled was going to be multiplied by 0 to equal 0. Am I wrong in doing it this way?

[@CasaErwin]

But you can't just choose arbitrarily. Either one of the factors could be 0. Therefore, as with all quatratic equations, you have two solutions: x = -1 or x = -5/4.

[@DayanandPandey-ns5qc]

Asn.-5/4 and -1

[@jessietucker9342]

-1?