\(\left(x-1\right)\left(x+2\right)\left(x+3\right)\left(x+6\right)=\left[\left(x-1\right)\left(x+6\right)\right]\left[\left(x+2\right)\left(x+3\right)\right]=\left(x^2+5x-6\right)\left(x^2+5x+6\right)=\left(x^2+5x\right)^2-6^2\ge0-36=-36\Rightarrow GTNNla:-36\Leftrightarrow x^2+5x=0\Leftrightarrow\left(x+\frac{5}{2}\right)^2=\frac{25}{4}\Leftrightarrow\left[{}\begin{matrix}x=0\\x=-5\end{matrix}\right.\)