\(\Leftrightarrow x^3-6x^2+12x-8+8x^3+12x^2+6x+1-9\left(x^3+3x^2+3x+1\right)=-16\)
\(\Leftrightarrow9x^3+6x^2+18x-7-9x^3-27x^2-27x-9=-16\)
\(\Leftrightarrow-21x^2-9x=0\)
\(\Leftrightarrow-3x\left(7x+3\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=-\dfrac{3}{7}\end{matrix}\right.\)