Answer
$\color{blue}{\left\{-\frac{3}{2}, 0\right\}}$
Work Step by Step
Factor out $\dfrac{1}{5}x$ to obtain:
\begin{align*}
\frac{1}{5}x\left(2x+3\right)&=0
\end{align*}
Use the Zero-Product Property by equating each factor to zero.
Then, solve each equation to obtain:
\begin{align*}
\frac{1}{5}x&=0 &\text{or}& &2x+3&=0\\\\
x&=0 &\text{or}& &2x=-3\\\\
x&=0 &\text{or}& &x=-\frac{3}{2}\\\\
\end{align*}
Therefore, the solution set is $\color{blue}{\left\{-\frac{3}{2}, 0\right\}}$.
