Answer
$x=\left\{ 0,\dfrac{1}{4} \right\}$
Work Step by Step
Using the properties of equality, the given equation is equivalent to
\begin{array}{l}\require{cancel}
8x^2=2x
\\\\
8x^2-2x=0
.\end{array}
Factoring the $GCF=2x,$ the equation above is equivalent to
\begin{array}{l}\require{cancel}
8x^2-2x=0
\\\\
2x(4x-1)=0
.\end{array}
Equating each factor to zero (Zero Product Property), then
\begin{array}{l}\require{cancel}
2x=0
\\\\\text{OR}\\\\
4x-1=0
.\end{array}
Solving each equation results to
\begin{array}{l}\require{cancel}
2x=0
\\\\
x=\dfrac{0}{2}
\\\\
x=0
\\\\\text{OR}\\\\
4x-1=0
\\\\
4x=1
\\\\
x=\dfrac{1}{4}
.\end{array}
Hence, the solutions are $
x=\left\{ 0,\dfrac{1}{4} \right\}
.$
