\(x^2+5x+6=0\\ \Leftrightarrow x^2+2x+3x+6=0\\ \Leftrightarrow\left(x^2+2x\right)+\left(3x+6\right)=0\\ \Leftrightarrow x\left(x+2\right)+3\left(x+2\right)=0\\ \Leftrightarrow\left(x+3\right)\left(x+2\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x+3=0\\x+2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-3\\x=-2\end{matrix}\right.\)
Vậy \(x=-2\) hoặc \(x=-3\)