Answer
$q=\left\{ -\dfrac{5}{2},\dfrac{4}{3} \right\}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given equation, $
(3q-4)(2q+5)=0
,$ use the Zero-Factor Property by equating each factor to zero. Then solve each equation.
$\bf{\text{Solution Details:}}$
Equating each factor of the equation above to zero (Zero-Factor Property), then
\begin{array}{l}\require{cancel}
3q-4=0
\text{ OR }
2q+5=0
.\end{array}
Using the properties of equality to solve each of the equation above results to
\begin{array}{l}\require{cancel}
3q-4=0
\\\\
3q=4
\\\\
q=\dfrac{4}{3}
\\\\\text{ OR }\\\\
2q+5=0
\\\\
2q=-5
\\\\
q=-\dfrac{5}{2}
.\end{array}
Hence, the solutions are $
q=\left\{ -\dfrac{5}{2},\dfrac{4}{3} \right\}
.$