Intermediate Algebra (12th Edition)

$x=\{ -10,5 \}$
$\bf{\text{Solution Outline:}}$ To solve the given equation, $(x+10)(x-5)=0 ,$ use the Zero-Factor Property by equating each factor to zero. Then solve each equation. $\bf{\text{Solution Details:}}$ Equating each factor of the equation above to zero (Zero-Factor Property), then \begin{array}{l}\require{cancel} x+10=0 \text{ OR } x-5=0 .\end{array} Using the properties of equality to solve each of the equation above results to \begin{array}{l}\require{cancel} x+10=0 \\\\ x=-10 \\\\\text{ OR }\\\\ x-5=0 \\\\ x=5 .\end{array} Hence, the solutions are $x=\{ -10,5 \} .$