# Solving Equations by Factoring

In this video, we are going to look at solving equations by factoring.To solve equations by factoring, we must make sure that the quadratic is set equal to 0.
For example:
If we are given the equation
$x^2+5x+6=0$
we can first factor like normal. We need two numbers that add up to 5 and multiply to 6. These two numbers are 2 and 3. So we are left with
$(x+2)(x+3)=0$
Now if we think about this logically, for two numbers to multiply together to give us 0, then at least one of these numbers must be 0. This means that either x+2 must equal 0 or x+3 must equal 0. So if we set each equal to 0 we get
$x+2=0$ and $x+3=0$
When we solve both of these by simply subtracting 2 and subtracting 3, we get that
$x=-2,-3$
If we had something more complicated like
$x^2+3x+4=14$
then the first step would be to subtract the 14 from both sides to make sure that our equation is set equal to 0. So now we are left with
$x^2+3x-10=0$
From here we can factor and solve. Two numbers that add up to 3 and multiply to -10 are 5 and -2, so
$(x+5)(x-2)=0$
From here, we set each factor equal to 0
$x+5=0$ and $x-2=0$
and solve by subtracting 5 and adding 2 to get
$x=-5,2$