Answer
\[\left\{ -3,8 \right\}\].
Work Step by Step
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\[\left\{ -3,8 \right\}\].
