${x}^{2}+3x+2x+6=4x+18$
${x}^{2}+5x+6=4x+18$
${x}^{2}+5x+6-4x-18=0$
${x}^{2}+x+6-18=0$
${x}^{2}+x-12=0$
${x}^{2}+4x-3x-12=0$
$x \times \left( x+4 \right)-3x-12=0$
$x \times \left( x+4 \right)-3\left( x+4 \right)=0$
$\left( x+4 \right) \times \left( x-3 \right)=0$
$\begin{array} { l }x+4=0,\\x-3=0\end{array}$
$\begin{array} { l }x=-4,\\x-3=0\end{array}$
$\begin{array} { l }x=-4,\\x=3\end{array}$
$\begin{array} { l }x_1=-4,& x_2=3\end{array}$