# The equation 2x^2-2x-12=0 is factored. Each factor is set equal to zero. What are these two equations?

Nov 26, 2016

First step: you can take $2$ out.

#### Explanation:

$\to 2 \left({x}^{2} - x - 6\right)$

Now we need to find two numbers that add up to $- 1$ and have a product of $- 6$. These turn out to be $- 3 \mathmr{and} + 2$

We then go to:
$2 \left(x - 3\right) \left(x + 2\right) = 0$

One of these factors needs to be $= 0$, so:
$x - 3 = 0 \to x = 3$, or
$x + 2 = 0 \to x = - 2$