${z}^{2}+11z+30=0$
Write $11z$ as a sum${z}^{2}+6z+5z+30=0$
Factor out $z$ from the expression$z \times \left( z+6 \right)+5z+30=0$
Factor out $5$ from the expression$z \times \left( z+6 \right)+5\left( z+6 \right)=0$
Factor out $z+6$ from the expression$\left( z+6 \right) \times \left( z+5 \right)=0$
When the product of factors equals $0$, at least one factor is $0$$\begin{array} { l }z+6=0,\\z+5=0\end{array}$
Solve the equation for $z$$\begin{array} { l }z=-6,\\z+5=0\end{array}$
Solve the equation for $z$$\begin{array} { l }z=-6,\\z=-5\end{array}$
The excluded values of the initial expression are $\begin{array} { l }-6,& -5\end{array}$$\begin{array} { l }z=-6,& z=-5\end{array}$