\(8x^3-12x^2+6x-9=0\)
\(\Leftrightarrow4x^2\left(2x-3\right)+3\left(2x-3\right)=0\)
\(\Leftrightarrow\left(2x-3\right)\left(4x^2+3\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}4x^2+3=0\left(vn\right)\\2x-3=0\end{matrix}\right.\)
\(\Rightarrow x=\frac{3}{2}\)
\(8x^3-12x^2+6x=9\)
\(\Leftrightarrow\left(2x\right)^3-3.\left(2x\right)^2.1+3.2x.1^2-1^3=9-1=8\)
\(\Leftrightarrow\left(2x-1\right)^3=8=2^3\)
\(\Rightarrow2x-1=2\Leftrightarrow2x=3\Leftrightarrow x=\frac{3}{2}\)