How do you do y^2+3y+2=0?

I know how to factor it, but now that it has a =0 after it, i am a little confused of what to do with it.

Any help will be greatly appreciated!

Thank you!

How do you do y^2+3y+2=0?

I know how to factor it, but now that it has a =0 after it, i am a little confused of what to do with it.

Any help will be greatly appreciated!

Thank you!

Tutors, please sign in to answer this question.

So, once you factor the left side of this equation it works out to be: (y+2)(y+1)=0

Now what do you do with this =0 part?

The Zero Product property states that when you multiply anything by 0, the answer will be zero.

So if you have an equation like a*b=0, you know that either a=0 or b=0, or both, in order to result in 0.

The factored version of your equation is in this same format.

In order to solve for y, you must set each factor equal to zero.

y+2=0 and y+1=0

Then you subtract each to find that y=-2 and y=-1

You can take these two answers and check them by plugging them back into the original equation

(-2)^2+3(-2)+2=0

4-6+2=0

0=0

(-1)^2+3(-1)+2=0

1-3+2=0

0=0

I hope this helps!

If you know how to factor it, you're more than half way there.

y^{2} + 3y + 2 can be factored as (y+2)(y+1) so the equation becomes:

(y+2)(y+1) = 0

Now you have a product of two real numbers equal to zero. This happens if and only if one of the factors is zero, that is:

(y+2) = 0 or (y+1) = 0

And then you have two solutions: x = -2 and x = -1.

Hope this helps!

## Comments

Totally makes sense now!

Thank you!

You're very welcome