\(\left(x-2\right)^3+\left(5-2x\right)^3=0\)
\(\Leftrightarrow\left(x-2+5-2x\right)\left[\left(x-2\right)^2-2\left(x-2\right)\left(5-2x\right)+\left(5-2x\right)^2\right]=0\)
\(\Leftrightarrow\left(3-x\right)\left(x^2-4x+4-2\left(5x-2x^2-10+4x\right)+25-20x+4x^2\right)=0\)
\(\Leftrightarrow\left(3-x\right)\left(x^2-4x+4-10x+4x^2+20-8x+25-20x+4x^2\right)=0\)
\(\Leftrightarrow\left(3-x\right)\left(9x^2-42x+49\right)=0\)
\(\Leftrightarrow\left(3-x\right)\left(x-\frac{7}{3}\right)^2=0\)
\(\Leftrightarrow\left[{}\begin{matrix}\left(3-x\right)=0\\\left(x-\frac{7}{3}\right)^2=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=3\\x=\frac{7}{3}\end{matrix}\right.\)
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