Ta có: \(4\left(x+5\right)\left(x+6\right)\left(x+10\right)\left(x+12\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x+5=0\\x+6=0\\x+10=0\\x+12=0\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}x=-5\\x=-6\\x=-10\\x=-12\end{matrix}\right.\)
Vậy \(x\in\left\{-5;-6;-10;-12\right\}\)