Evaluate: x^2+2x-24=0

Expression: ${x}^{2}+2x-24=0$

Write $2x$ as a difference

${x}^{2}+6x-4x-24=0$

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

$\begin{array} { l }x_1=-6,& x_2=4\end{array}$