Answer
$y=\left\{ -\dfrac{3}{2},\dfrac{5}{2} \right\}$
Work Step by Step
Factoring the given equation, $
4y^2=7y+15
,$ results to
\begin{array}{l}\require{cancel}
4y^2-7y-15=0
\\\\
(2y+3)(2y-5)=0
.\end{array}
Equating each factor to zero (Zero Product Principle), then the solutions to the equation, $
(2y+3)(2y-5)=0
,$ are
\begin{array}{l}\require{cancel}
2y+3=0
\\\\
2y=-3
\\\\
y=-\dfrac{3}{2}
,\\\\\text{OR}\\\\
2y-5=0
\\\\
2y=5
\\\\
y=\dfrac{5}{2}
.\end{array}
Hence, $
y=\left\{ -\dfrac{3}{2},\dfrac{5}{2} \right\}
.$
