${m}^{2}+2m-7m-14=0$
Factor out $m$ from the expression$m \times \left( m+2 \right)-7m-14=0$
Factor out $-7$ from the expression$m \times \left( m+2 \right)-7\left( m+2 \right)=0$
Factor out $m+2$ from the expression$\left( m+2 \right) \times \left( m-7 \right)=0$
When the product of factors equals $0$, at least one factor is $0$$\begin{array} { l }m+2=0,\\m-7=0\end{array}$
Solve the equation for $m$$\begin{array} { l }m=-2,\\m-7=0\end{array}$
Solve the equation for $m$$\begin{array} { l }m=-2,\\m=7\end{array}$
The equation has $2$ solutions$\begin{array} { l }m_1=-2,& m_2=7\end{array}$