## Intermediate Algebra (12th Edition)

$x=\left\{ 0,\dfrac{5}{3} \right\}$
$\bf{\text{Solution Outline:}}$ 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, $x=\left\{ 0,\dfrac{5}{3} \right\} .$