# How do you solve x² + x = 6?

Mar 24, 2016

$x = - 3 , 2$

#### Explanation:

${x}^{2} + x = 6$ => Subtract 6 from both sides:
${x}^{2} + x - 6 = 0$ => $x = 3 x - 2 x$:
${x}^{2} + 3 x - 2 x - 6 = 0$ => factor by grouping:
$x \left(x + 3\right) - 2 \left(x + 3\right) = 0$
$\left(x + 3\right) \left(x - 2\right) = 0$
The Zero Product Property: if ab=0, then either a=0  or  b=0, or both.
$x + 3 = 0$ => $x = - 3$
$x - 2 = 0$ => $x = 2$