Phương trình \(\left(m^2+5m+6\right)x+m+3=0\Leftrightarrow\left\{\begin{matrix}m^2+5m+6=0\\m+3\ne0\end{matrix}\right.\)
\(\Leftrightarrow\left\{\begin{matrix}m^2+2m+3m+6=0\\m+3\ne0\end{matrix}\right.\)
\(\Leftrightarrow\left\{\begin{matrix}m\left(m+2\right)+3\left(m+2\right)=0\\m+3\ne0\end{matrix}\right.\)
\(\Leftrightarrow\left\{\begin{matrix}\left(m+2\right)\left(m+3\right)=0\\m+3\ne0\end{matrix}\right.\)
\(\Leftrightarrow\left\{\begin{matrix}\left[\begin{matrix}m+2=0\\m+3=0\end{matrix}\right.\\m\ne-3\end{matrix}\right.\)
\(\Leftrightarrow\left\{\begin{matrix}\left[\begin{matrix}m\ne-2\left(TMĐK\right)\\m\ne-3\left(KTMĐK\right)\end{matrix}\right.\\m\ne-3\end{matrix}\right.\)
Vậy m = -2
