#### Answer

$x=-7~~$ or $~~x=2$

#### Work Step by Step

Let's consider a trinomial in this form: $~x^2+bx+c$
To factor this trinomial, we need to find two numbers $r$ and $s$ such that $r+s = b$ and $r\times s = c$
Then we can factor the trinomial as follows:
$~x^2+bx+c = (x+r)~(x+s)$
We can use the GCF to factor the left side of the given equation:
$8x^2+40x-112=0$
$(8)~(x^2+5x-14)=0$
To factor the left side of the equation, we need to find two numbers $r$ and $s$ such that $r+s = 5$ and $r\times s = -14$. We can see that $(7)+(-2) = 5~$ and $(7)\times (-2) = -14$
We can solve the equation as follows:
$8x^2+40x-112=0$
$(8)~(x^2+5x-14)=0$
$(8)~(x+7)(x-2)=0$
$x=-7~~$ or $~~x=2$