Solve for: m^2-5m-14=0

Expression: ${m}^{2}-5m-14=0$

Write $-5m$ as a difference

${m}^{2}+2m-7m-14=0$

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

$\begin{array} { l }m_1=-2,& m_2=7\end{array}$