Evaluate: x^2-3x-10=0

Expression: ${x}^{2}-3x-10=0$

Write $-3x$ as a difference

${x}^{2}+2x-5x-10=0$

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

$\begin{array} { l }x_1=-2,& x_2=5\end{array}$