Answer
$z=\left\{ 0,\dfrac{4}{3} \right\}$
Work Step by Step
Using the properties of equality, the given expression, $
15z^2+7=20z+7
,$ is equivalent to
\begin{array}{l}\require{cancel}
15z^2-20z+7-7=0
\\\\
15z^2-20z=0
.\end{array}
Factoring the above equation, $
15z^2-20z=0
,$ results to
\begin{array}{l}\require{cancel}
5z(3z-4)
.\end{array}
Equating each factor to zero (Zero Product Principle), then the solutions to the equation, $
5z(3z-4)
,$ are
\begin{array}{l}\require{cancel}
5z=0
\\\\
z=\dfrac{0}{5}
\\\\
z=0
,\\\\\text{OR}\\\\
3z-4=0
\\\\
3z=4
\\\\
z=\dfrac{4}{3}
.\end{array}
Hence, $
z=\left\{ 0,\dfrac{4}{3} \right\}
.$
