\(x^3-4x^2-9x+36=0\)
\(\Leftrightarrow x^2\left(x-4\right)-9\left(x-4\right)=0\)
\(\Leftrightarrow\left(x-4\right)\left(x^2-9\right)=0\)
\(\Leftrightarrow\left(x-4\right)\left(x-3\right)\left(x+3\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-4=0\\x-3=0\\x+3=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=4\\x=3\\x=-3\end{matrix}\right.\)