\(x^2-4+\left(x-2\right)\left(x+3\right)=0\)
\(\Leftrightarrow\left(x-2\right)\left(x+2\right)+\left(x+3\right)\left(x+2\right)=0\)
\(\Leftrightarrow\left(x+2\right)\left(x-2+x+3\right)=0\)
\(\Leftrightarrow\left(x+2\right)\left(2x+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x+2=0\\2x+1=0\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=-2\\x=-\frac{1}{2}\end{matrix}\right.\)