Answer
$\color{blue}{\left\{-\frac{5}{2}, 0, \frac{9}{4}\right\}}$
Work Step by Step
RECALL:
Zero-Factor Property:
If $ab = 0$, then either $a=0$ or $b=0$ or both are $0$.
Use the property above to obtain:
\begin{array}{ccccc}
&-3x=0 &\text{or} &2x+5=0 &\text{or} &4x-9=0
\end{array}
Solve each equation to obtain:
$-3x=0
\\\frac{-3x}{-3}=\frac{0}{-3}
\\x=0$
or
$2x+5=0
\\2x=-5
\\\frac{2x}{2}=\frac{-5}{2}
\\x=-\frac{5}{2}$
or
$4x-9=0
\\4x=0+9
\\4x=9
\\\frac{4x}{4}=\frac{9}{4}
\\x=\frac{9}{4}$
Thus, the solution set is $\color{blue}{\left\{-\frac{5}{2}, 0, \frac{9}{4}\right\}}$.
