${x}^{2}+6x-4x-24=0$
Factor out $x$ from the expression$x \times \left( x+6 \right)-4x-24=0$
Factor out $-4$ from the expression$x \times \left( x+6 \right)-4\left( x+6 \right)=0$
Factor out $x+6$ from the expression$\left( x+6 \right) \times \left( x-4 \right)=0$
When the product of factors equals $0$, at least one factor is $0$$\begin{array} { l }x+6=0,\\x-4=0\end{array}$
Solve the equation for $x$$\begin{array} { l }x=-6,\\x-4=0\end{array}$
Solve the equation for $x$$\begin{array} { l }x=-6,\\x=4\end{array}$
The equation has $2$ solutions$\begin{array} { l }x_1=-6,& x_2=4\end{array}$