Answer
$k=\left\{ -\dfrac{8}{3},\dfrac{5}{2} \right\}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given equation, $
(2k-5)(3k+8)=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}
2k-5=0
\text{ OR }
3k+8=0
.\end{array}
Using the properties of equality to solve each of the equation above results to
\begin{array}{l}\require{cancel}
2k-5=0
\\\\
2k=5
\\\\
k=\dfrac{5}{2}
\\\\\text{ OR }\\\\
3k+8=0
\\\\
3k=-8
\\\\
k=-\dfrac{8}{3}
.\end{array}
Hence, the solutions are $
k=\left\{ -\dfrac{8}{3},\dfrac{5}{2} \right\}
.$