Answer
$x=\left\{ 0,\dfrac{5}{3} \right\}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given eqution, $
3x^2-5x=0
,$ express the equation in factored form. Then, equate each factor to zero (Zero Product Property). Finally, solve each equation.
$\bf{\text{Solution Details:}}$
Factoring the $GCF=x,$ the equation above is equivalent to
\begin{array}{l}\require{cancel}
x(3x-5)=0
.\end{array}
Equating each factor to zero (Zero Product Property), the solutions to the equation above are
\begin{array}{l}\require{cancel}
x=0
\\\\\text{OR}\\\\
3x-5=0
.\end{array}
Solving each equation results to
\begin{array}{l}\require{cancel}
x=0
\\\\\text{OR}\\\\
3x-5=0
\\\\
3x=5
\\\\
x=\dfrac{5}{3}
.\end{array}
Hence, $
x=\left\{ 0,\dfrac{5}{3} \right\}
.$
