# How do you solve 6x^2 - 5x - 56 = 0 by factoring?

Oct 5, 2015

$\left(3 x + 8\right) \left(2 x - 7\right) = 0$

$x = - \frac{8}{3}$ or $x = \frac{7}{2}$

#### Explanation:

Problems like this take practice.
Undoing the FOIL method I try to look for factors where the product of the last terms is 56.

(?+8)(?+7)=0

The middle term is $- 5 x$ so I take a guess that the first terms are
$3 x$ and $2 x$ but I have to account for the negative signs so I have

$\left(3 x + 8\right) \left(2 x - 7\right) = 0$

$3 x + 8 = 0$ or $2 x - 7 = 0$

$3 x = - 8$

$x = - \frac{8}{3}$

$2 x = 7$

$x = \frac{7}{2}$