\(2x\left(3x-1\right)-6x+2=0\)
\(\Leftrightarrow2x\left(3x-1\right)-2\left(3x-1\right)=0\)
\(\Leftrightarrow\left(3x-1\right)\left(2x-2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}3x-1=0\\2x-2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{3}\\x=1\end{matrix}\right.\)