Answer
\[\left\{ -11,5 \right\}\].
Work Step by Step
Consider the expression\[\left( x+11 \right)\left( x-5 \right)=0\].
Then, by the zero product principal either \[\left( x+11 \right)=0\]or\[\left( x-5 \right)=0\].
Now \[\left( x+11 \right)=0\]implies that \[x=-11\]and \[\left( x-5 \right)=0\] implies that\[x=5\].
Next, check the proposed solution by substituting it in the original equation.
Check for\[x=-11\]. So consider,
\[\begin{align}
& \left( x+11 \right)\left( x-5 \right)=0 \\
& \left( -11+11 \right)\left( -11-5 \right)=0 \\
& 0\left( -16 \right)=0 \\
& 0=0
\end{align}\]
Now check for\[x=5\]. So consider,
\[\begin{align}
& \left( x+11 \right)\left( x-5 \right)=0 \\
& \left( 5+11 \right)\left( 5-5 \right)=0 \\
& 16\left( 0 \right)=0 \\
& 0=0
\end{align}\]
Hence, the solution set is\[\left\{ -11,5 \right\}\].