# Thread: Which side to set to zero

1. ## Which side to set to zero

Hi. when adding equations i.e. 3x = -7x^2+9 which side do I set to zero? I have come across multiple problems where sometimes the left side is set to zero and sometimes the right side is set to zero. Thanks for any help!!

2. Originally Posted by Mathfailure
Hi. when adding equations i.e. 3x = -7x^2+9 which side do I set to zero? I have come across multiple problems where sometimes the left side is set to zero and sometimes the right side is set to zero. Thanks for any help!!
It does not matter (so you do whichever is easier).

In this case we have:

3x = -7x^2+9

so subtracting 3x from both sides we get:

0 = -7x^2 - 3x + 9

or subtracting -7x^2+9 from both sides we get:

7x^2 + 3x - 9 = 0.

These two can then be transformed into one another by switching
the equlities around and multiplying by -1.

Note: 7x^2 + 3x - 9 = 0 is the same thing as 0 = 7x^2 + 3x - 9.

RonL

3. ## Re:

Originally Posted by Mathfailure
Hi. when adding equations i.e. 3x = -7x^2+9 which side do I set to zero? I have come across multiple problems where sometimes the left side is set to zero and sometimes the right side is set to zero. Thanks for any help!!
Hello MathFailure it's your choice, but I tend to move everything over to the left for two reasons:

1. In English we read from Left to Right
2. It tends to be a bit neater

You will get the same solutions either way, and like I said it's your choice!

4. I guess this one is a bit confusing to me

4x+12-5x-25=-6x^2-48x-90

I keep getting conflicting answeres when I set the right side to 0 versus the left side to 0.

5. Originally Posted by Mathfailure
I guess this one is a bit confusing to me

4x+12-5x-25=-6x^2-48x-90

I keep getting conflicting answeres when I set the right side to 0 versus the left side to 0.
Be careful with your signs and you should have no problems:

4x + 12 - 5x - 25 = -6x^2 - 48x - 90

First (always) combine like terms:

-x - 13 = -6x^2 - 48x - 90

Now move terms.

If we move the terms to the right, we get
-6x^2 - 48x + x - 90 + 13 = 0
-6x^2 - 47x - 77 = 0 ... multiply everything by -1
6x^2 + 47x + 77 = 0

If we move the terms to the left, we get
6x^2 - x + 48x - 13 + 90 = 0
6x^2 + 47x + 77 = 0

Notice that the two answers became the same (if I multiply one version by -1, that is).

6. Originally Posted by ecMathGeek
Be careful with your signs and you should have no problems:

4x + 12 - 5x - 25 = -6x^2 - 48x - 90

First (always) combine like terms:

-x - 13 = -6x^2 - 48x - 90

Now move terms.

If we move the terms to the right, we get
-6x^2 - 48x + x - 90 + 13 = 0
-6x^2 - 47x - 77 = 0 ... multiply everything by -1
6x^2 + 47x + 77 = 0

If we move the terms to the left, we get
6x^2 - x + 48x - 13 + 90 = 0
6x^2 + 47x + 77 = 0

Notice that the two answers became the same (if I multiply one version by -1, that is).

Do we only multiply by -1 if we move the terms to the right? Just curious because I have been moving all terms to the left and have not multiplied by -1 and my final solutions have turned out after using the quadratic forumula and/or factoring. Thanks..

7. Originally Posted by Mathfailure
Do we only multiply by -1 if we move the terms to the right? Just curious because I have been moving all terms to the left and have not multiplied by -1 and my final solutions have turned out after using the quadratic forumula and/or factoring. Thanks..
you don't have to multiply by -1 if you don't want to, ecMathGeek was just illustrating it doesn't matter what side you bring everything on, everything will work out to be the same.

also, it's not aesthetic to have a minus in front, so whatever side you decide to solve on, if there is a minus sign in the front, you usually multply by -1 to change it to plus. it does not change the equality to do that

so to answer your question directly, no, it is not always the case that we multiply by -1 if we move to the right, its a matter of convenience and looking good while we're doing math