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