Question 73624
Well, there are a couple of discrepancies I see here.
1) Although your first equation is written as:
x(x+1)=-2(x-4)=2, I assume that there is a typo and that you meant to write:
{{{x(x+1) = -2(x-4)+2}}} Right?
The second thing that I notice is that you have not handled the (+ & -) signs correctly.  Let's step through the process:
{{{x(x+1) = -2(x-4)+2}}} Apply the distributive property to both sides.
{{{x^2+x = -2x+8+2}}} Combine like-terms.
{{{x^2+3x = 10}}} Subtract 10 from both sides.
{{{x^2+3x-10 = 0}}} Factor this quadratic equation.
{{{(x-2)(x+5) = 0}}} Apply the zero product principle.
{{{x-2 = 0}}} and/or {{{x+5 = 0}}}
Solutions:
x = 2 or x = -5