Question 17435
Hi, to make this easier to see it would be helpful to divide both sides by -2 first:
factor out -2 first
{{{-2x^2 - 2x + 24}}} = {{{-2(x^2 + x -12)}}}
so we have
{{{x^2 + x - 12}}} = 0
from this we see
{{{x^2 + x - 12}}} = (x+4)(x+3) = 0
so this equation will be true if either x+4 = 0 or x+3 = 0
so possibilities for x are -4 or -3.

Hope this helps.