\(2x\left(x+2\right)^2-8x^2=2\left(x-2\right)\left(x^2+2x+4\right)\)
\(\Leftrightarrow2x\left(x^2+4x+4\right)-8x^2=2\left(x^3-8\right)\)
\(\Leftrightarrow2x^3+8x=2\left(x^3-8\right)\)
\(\Leftrightarrow2\left(x^3+4x\right)=2\left(x^3-8\right)\)
\(\Leftrightarrow x=-2\)