Let's first simplify both sides of the equation:

2(x+4) - x(x-5) = 7(x-8)

Expanding the left side:
2x + 8 - x^2 + 5x = 7x - 56

Combine like terms:
2x + 8 - x^2 + 5x = 7x - 56
7x + 8 - x^2 = 7x - 56

Now, move all terms to one side of the equation:
7x + 8 - x^2 - 7x + 56 = 0
-x^2 + 64 = 0

Now, we need to solve for x:
-x^2 + 64 = 0
-x^2 = -64
x^2 = 64
x = ± 8

Therefore, the solution to the equation is x = 8 or x = -8.