\(\Leftrightarrow x^3-8x^2+7x+2x^2-16x+14=0\)
\(\Leftrightarrow x\left(x^2-8x+7\right)+2\left(x^2-8x+7\right)=0\)
\(\Leftrightarrow\left(x+2\right)\left(x^2-8x+7\right)=0\)
\(\Leftrightarrow\left(x+2\right)\left(x-1\right)\left(x-7\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=-2\\x=1\\x=7\end{matrix}\right.\)