\(\left(3x-1\right)^{2013}=\left(3x-1\right)^{2015}\)
\(\Leftrightarrow\left(3x-1\right)^{2013}-\left(3x-1\right)^{2015}=0\)
\(\Leftrightarrow\left(3x-1\right)^{2013}\cdot\left[1-\left(3x-1\right)^2\right]=0\)
\(\Leftrightarrow\left(3x-1\right)^{2013}\left(1-3x+1\right)\left(1+3x-1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}3x-1=0\\-3x+2=0\\3x=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{3}\\x=\dfrac{2}{3}\\x=0\end{matrix}\right.\)
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