$(x-2)^3+(5-2x)^3=0_{}$

$⇔x^3-6x^2+12x-8+125-150x+60x^2-8x^3=0_{}$

$⇔-7x^3+54x^2-138x+117=0_{}$

$⇔-7x^3+21x^2+33x^2-99x-39x+117=0_{}$

$⇔-7x^2.(x-3)+33x.(x-3)-39.(x-3)=0_{}$

$⇔-(x-3).(7x^2-33x+39)=0_{}$

$⇔(x-3).(7x^2-33x+39)=0_{}$

$⇔_{}$ \(\left[ \begin{array}{l}x-3=0\\7x^2-33x+39=0\end{array} \right.\) $⇔_{}$ \(\left[ \begin{array}{l}x=3\\x∉R\end{array} \right.\)

$Vậy_{}$ $x=3_{}$

$(x-2)^3+(5-2x)^3=0_{}$

`=>` $x^3-6x^2+12x-8+125-150x+60x^2-8x^3=0_{}$

`=>`$-7x^3+54x^2-138x+117=0_{}$

`=>`$7x^3+21x^2+33x^2-99x-39x+117=0_{}$

$⇔-7x^2.(x-3)+33x.(x-3)-39.(x-3)=0_{}$

$⇔(x-3).(7x^2-33x+39)=0_{}$

$⇔_{}$ \(\left[ \begin{array}{l}x-3=0\\7x^2-33x+39=0\end{array} \right.\) $⇔_{}$ \(\left[ \begin{array}{l}x=3\\loại\end{array} \right.\)

$Vậy_{}$ $x=3_{}$