#### Answer

$x=\left\{ -\dfrac{5}{3},\dfrac{1}{3} \right\}$

#### Work Step by Step

Taking the square root of both sides (the Square Root Property), the solutions to the given equation, $
(3x+2)^2=9
,$ are
\begin{array}{l}\require{cancel}
(3x+2)=\pm\sqrt{9}
\\\\
3x+2=\pm\sqrt{(3)^2}
\\\\
3x+2=\pm3
\\\\
3x=-2\pm3
\\\\
x=\dfrac{-2\pm3}{3}
.\end{array}
Hence, $
x=\left\{ -\dfrac{5}{3},\dfrac{1}{3} \right\}
.$