\(\left(2\cdot5^{x-2}-50\right)\left(3x+6\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}2\cdot5^x=50\\3x+6=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}5^x=25=5^2\\3x=-6\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\\x=-2\end{matrix}\right.\)