Answer
$x=\left\{ -\dfrac{1}{10},\dfrac{1}{27} \right\}$
Work Step by Step
Equating each factor to zero (Zero Product Principle), then the solutions to the equation, $
\left( \dfrac{1}{9}-3x \right)\left( \dfrac{1}{5}+2x \right)=0
,$ is
\begin{array}{l}\require{cancel}
\dfrac{1}{9}-3x=0
\\\\
-3x=-\dfrac{1}{9}
\\\\
x=\dfrac{-\dfrac{1}{9}}{-3}
\\\\
x=\dfrac{1}{27}
,\\\\\text{OR}\\\\
\dfrac{1}{5}+2x=0
\\\\
2x=-\dfrac{1}{5}
\\\\
x=-\dfrac{\dfrac{1}{5}}{2}
\\\\
x=-\dfrac{1}{10}
.\end{array}
Hence, $
x=\left\{ -\dfrac{1}{10},\dfrac{1}{27} \right\}
.$
