# How do you solve x^2 - x - 12 = 0 by factoring?

Aug 16, 2015

The solutions are
 color(blue)(x=-3
color(blue)(x=4

#### Explanation:

x^2−x−12=0

We can Split the Middle Term of this expression to factorise it and thereby find solutions.

In this technique, if we have to factorise an expression like $a {x}^{2} + b x + c$, we need to think of 2 numbers such that:

${N}_{1} \cdot {N}_{2} = a \cdot c = 1 \cdot - 12 = - 12$
AND
${N}_{1} + {N}_{2} = b = - 1$

After trying out a few numbers we get ${N}_{1} = 3$ and ${N}_{2} = - 4$
$3 \cdot - 4 = - 12$, and $3 + \left(- 4\right) = - 1$

x^2−x−12=x^2−4x+3x−12

x(x-4) +3(x−4)=0

$\left(x + 3\right) \left(x - 4\right) = 0$

Now we equate the factors to zero.
x+3 = 0 , color(blue)(x=-3
x-4 = 0 , color(blue)(x=4