\(3x\left(x+2\right)\left(x-2\right)-\left(x+3\right)\left(x^2-3x+9\right)=6x-27\)
\(\Leftrightarrow3x^3-12x-x^3-27-6x+27=0\)
\(\Leftrightarrow2x^3-18x=0\)
\(\Leftrightarrow x^3-9x=0\)
\(\Leftrightarrow x\left(x^2-9\right)=0\)
\(\Leftrightarrow x\left(x-3\right)\left(x+3\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x-3=0\\x+3=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=3\\x=-3\end{matrix}\right.\)