Answer
$y=\left\{ -2, -\dfrac{4}{5} \right\}$
Work Step by Step
Equating each factor to zero (Zero-Product Property), then the values of $y$ that satisfy the given equation, $
(y+2)(5y+4)=0
,$ are
\begin{array}{l}\require{cancel}
y+2=0
\\\\
y=-2
,\\\\\text{OR}\\\\
5y+4=0
\\\\
5y=-4
\\\\
y=-\dfrac{4}{5}
.\end{array}
Hence, $
y=\left\{ -2, -\dfrac{4}{5} \right\}
.$
