# Chapter R - Elementary Algebra Review - R.5 Polynomials and Factoring - R.5 Exercise Set - Page 970: 39

$x=\{ 0,5 \}$

#### Work Step by Step

Dividing both sides by $2,$ the given expression is equivalent to \begin{array}{l}\require{cancel} 2x^2-10x=0 \\\\ \dfrac{2x^2-10x}{2}=\dfrac{0}{2} \\\\ x^2-5x=0 .\end{array} Factoring the $GCF=2x,$ the given expression is equivalent to \begin{array}{l}\require{cancel} 2x^2-10x=0 \\\\ 2x(x-5)=0 .\end{array} Equating each factor to zero (Zero Product Property), then \begin{array}{l}\require{cancel} 2x=0 \\\\\text{OR}\\\\ x-5=0 .\end{array} Solving each equation results to \begin{array}{l}\require{cancel} 2x=0 \\\\ x=\dfrac{0}{2} \\\\ x=0 \\\\\text{OR}\\\\ x-5=0 \\\\ x=5 .\end{array} Hence, the solutions are $x=\{ 0,5 \} .$

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