Answer
\begin{align*}x&=-\frac{10}{3} &\text{and}& &x=\frac{2}{3}
\end{align*}
Work Step by Step
Factor the trinomial to obtain:
\begin{align*}
(3x+4)(3x+4)&=36\\
(3x+4)^2&=6^2
\end{align*}
Take the square root of both sides:
\begin{align*}
\sqrt{3x+4)^2}&=\pm \sqrt{6^2}\\
3x+4&=\pm 6
\end{align*}
Solve for $x$:
\begin{align*}3x&=-4\pm 6\\\\
\frac{3x}{3}&=\frac{-4\pm6}{3}\\\\
x&=-\frac{4}{3} \pm 2
\end{align*}
Split the solutions to obtain:
\begin{align*}
x&=-\frac{4}{3}-2\\\\
x_1&=-\frac{4}{3}-\frac{6}{3}\\\\
x_1&=-\frac{10}{3}\\\\
\end{align*}
\begin{align*}
x&=-\frac{4}{3}+2\\\\
x_1&=-\frac{4}{3}+\frac{6}{3}\\\\
x_1&=\frac{2}{3}\\\\
\end{align*}