# Solve for: x^2+7x+12=0

## Expression: ${x}^{2}+7x+12=0$

Write $7x$ as a sum

${x}^{2}+4x+3x+12=0$

Factor out $x$ from the expression

$x \times \left( x+4 \right)+3x+12=0$

Factor out $3$ from the expression

$x \times \left( x+4 \right)+3\left( x+4 \right)=0$

Factor out $x+4$ from the expression

$\left( x+4 \right) \times \left( x+3 \right)=0$

When the product of factors equals $0$, at least one factor is $0$

$\begin{array} { l }x+4=0,\\x+3=0\end{array}$

Solve the equation for $x$

$\begin{array} { l }x=-4,\\x+3=0\end{array}$

Solve the equation for $x$

$\begin{array} { l }x=-4,\\x=-3\end{array}$

The equation has $2$ solutions

$\begin{array} { l }x_1=-4,& x_2=-3\end{array}$

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