First multiply (x + 8) times (x + 8) with FOIL (multiply the first terms, outside terms, inside terms and last terms). . .
x^2 + 8x + 8x + 64 = x^2 + 16x + 64
Now set that equal to the right side of the equation. . .
x^2 + 16x + 64 = 2x + 15
Subtract 2x from each side and subtract 15 from each side. . .
x^2 + 14x + 49 = 0
Now factor with reverse FOIL. . .
(x + 7) (x + 7) = 0
So x must equal -7
Plug that value back into the original problem to make sure it works.