Answer
$(x+3)(x-5)=0$
Work Step by Step
We rewrite the given equation by moving all terms to the left side and factoring:
$$\begin{align*}
x^2+(x+7)^2-(x+8)^2&=0\quad&&\text{Subtract }(x+8)^2\text{ from each side.}\\
x^2+x^2+14x+49-x^2-16x-64&=0\quad&&\text{Perform calculations.}\\
x^2-2x-15&=0\quad&&\text{Group terms and simplify.}\\
(x+3)(x-5)&=0\quad&&\text{Factor the left side.}
\end{align*}$$
