\(\left(2x\right)^3-\left(4x+1\right)^3+\left(2x+1\right)^3=0\)
\(\Leftrightarrow\left(-2x-1\right)\left(4x^2+8x^2+2x+16x^2+8x+1\right)+\left(2x+1\right)^3=0\)
\(\Leftrightarrow\left(2x+1\right)\left(\left(2x+1\right)^2-28x^2-10x-1\right)=0\)
\(\Leftrightarrow\left(2x+1\right)\left(4x^2+4x+1-28x^2-10x-1\right)=0\)
\(\Leftrightarrow\left(2x+1\right)\left(-24x^2-6x\right)=0\)
\(\Leftrightarrow-6x\left(2x+1\right)\left(4x+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\2x+1=0\\4x+1=0\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=\dfrac{-1}{2}\\x=\dfrac{-1}{4}\end{matrix}\right.\)
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