## Thinking Mathematically (6th Edition)

$\left\{ -3,8 \right\}$.
Consider the expression$\left( x-8 \right)\left( x+3 \right)=0$. Then, by the zero product principal either $\left( x-8 \right)=0$or$\left( x+3 \right)=0$. Now $\left( x-8 \right)=0$implies that $x=8$and $\left( x+3 \right)=0$ implies that$x=-3$. Next check the proposed solution by substituting it in the original equation. Check for$x=8$. So consider, \begin{align} & \left( x-8 \right)\left( x+3 \right)=0 \\ & \left( 8-8 \right)\left( 8+3 \right)=0 \\ & 0\left( 11 \right)=0 \\ & 0=0 \end{align} Now check for$x=-3$. So consider, \begin{align} & \left( x-8 \right)\left( x+3 \right)=0 \\ & \left( -3-8 \right)\left( -3+3 \right)=0 \\ & \left( -11 \right)0=0 \\ & 0=0 \end{align} Hence, the solution set is$\left\{ -3,8 \right\}$.