Answer
$z=\left\{ 0,\dfrac{3}{2} \right\}$
Work Step by Step
Using the properties of equality, the given expression, $
14z^2-3=21z-3
,$ is equivalent to
\begin{array}{l}\require{cancel}
14z^2-21z-3+3=0
\\\\
14z^2-21z=0
.\end{array}
Factoring the above equation, $
14z^2-21z=0
,$ results to
\begin{array}{l}\require{cancel}
7z(2z-3)=0
.\end{array}
Equating each factor to zero (Zero Product Principle), then the solutions to the equation, $
7z(2z-3)=0
,$ are
\begin{array}{l}\require{cancel}
7z=0
\\\\
z=\dfrac{0}{7}
\\\\
z=0
,\\\\\text{OR}\\\\
2z-3=0
\\\\
2z=3
\\\\
z=\dfrac{3}{2}
.\end{array}
Hence, $
z=\left\{ 0,\dfrac{3}{2} \right\}
.$
