# Chapter 5 - Polynomials and Factoring - 5.7 Solving Quadratic Equations by Factoring - 5.7 Exercise Set: 19

$x=\left\{ 50,70 \right\}$

#### Work Step by Step

Equating each factor to zero (Zero Product Principle), then the solutions to the equation, $(20-0.4x)(7-0.1x)=0 ,$ is \begin{array}{l}\require{cancel} 20-0.4x=0 \\\\ -0.4x=-20 \\\\ x=\dfrac{-20}{-0.4} \\\\ x=50 ,\\\\\text{OR}\\\\ 7-0.1x=0 \\\\ -0.1x=-7 \\\\ x=\dfrac{-7}{-0.1} \\\\ x=70 .\end{array} Hence, $x=\left\{ 50,70 \right\} .$

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