#### Answer

$\left\{-5, 5\right\}$

#### Work Step by Step

Write the equation in the form $ax^2+bx+c=0$ to obtain:
\begin{align*}
x^2+7x-9-7x-16&=0\\
x^2-25&=0\\
(x-5)(x+5)&=0\end{align*}
Use the Zero-Product Property by equating each factor to zero, then solving each equation to obtain:
\begin{align*}
x-5&=0 &\text{or}& &x+5=0\\
x&=5 &\text{or}& &x=-5\\
\end{align*}