\(\left(x^2-4\right)-3\left(x+2\right)=0\)
\(\Rightarrow\left(x-2\right)\left(x+2\right)-3\left(x+2\right)=0\)
\(\Rightarrow\left(x+2\right)\left(x-2-3\right)=0\)
\(\Rightarrow\left(x+2\right)\left(x-5\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x+2=0\\x-5=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=-2\\x=5\end{matrix}\right.\)