${x}^{2}+2x-5x-10=0$
Factor out $x$ from the expression$x \times \left( x+2 \right)-5x-10=0$
Factor out $-5$ from the expression$x \times \left( x+2 \right)-5\left( x+2 \right)=0$
Factor out $x+2$ from the expression$\left( x+2 \right) \times \left( x-5 \right)=0$
When the product of factors equals $0$, at least one factor is $0$$\begin{array} { l }x+2=0,\\x-5=0\end{array}$
Solve the equation for $x$$\begin{array} { l }x=-2,\\x-5=0\end{array}$
Solve the equation for $x$$\begin{array} { l }x=-2,\\x=5\end{array}$
The equation has $2$ solutions$\begin{array} { l }x_1=-2,& x_2=5\end{array}$