c) \(2\left(x-4\right)^2-\left(x-4\right)=0\)

\(\Rightarrow\left(x-4\right)\cdot\left[2\left(x-4\right)-1\right]=0\)

\(\Leftrightarrow\left(x-4\right)-\left(2x-8-1\right)=0\)

\(\Leftrightarrow\left(x-4\right)\left(2x-9\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x-4=0\\2x-9=0\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=4\\x=\dfrac{9}{2}\end{matrix}\right.\)

Vậy \(x_1=4;x_2=\dfrac{9}{2}\)

d) \(3x\left(x-1\right)+\left(x-1\right)^2=0\)

\(\Rightarrow\left(x-1\right)\left(3+x-1\right)=0\)

\(\Leftrightarrow\left(x-1\right)\left(2+x\right)=0\)

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

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

Vậy \(x_1=-2;x_2=1\)

d) \(5x\left(x-9\right)^2-\left(9-x\right)^3=0\)

\(\Rightarrow5x\left(x^2-18x+81\right)-\left(729-243x+27x^2-x^3\right)=0\)

\(\Leftrightarrow5x^3-90x^2+405x-729+243x-27x^2+x^3=0\)

\(\Leftrightarrow6x^3-117x^2+648x-729=0\)

\(\Leftrightarrow3\left(2x^3-39x^2+216x-243\right)=0\)

\(\Leftrightarrow3\left(2x^3-18x^2-21x^2+189x+27x-243\right)=0\)

\(\Leftrightarrow3\left(2x^2\cdot\left(x-9\right)-21\cdot\left(x-9\right)+27\left(x-9\right)\right)=0\)

\(\Leftrightarrow3\left(x-9\right)\left(2x^2-21x+27\right)=0\)

\(\Leftrightarrow3\left(x-9\right)\cdot\left(2x^2-38-18x+27\right)=0\)

\(\Leftrightarrow3\left(x-9\right)\cdot\left(x\cdot\left(2x-3\right)-9\left(2x-3\right)\right)=0\)

\(\Leftrightarrow3\left(x-9\right)\cdot\left(x-9\right)\cdot\left(2x-3\right)=0\)

\(\Leftrightarrow3\left(x-9\right)^2\cdot\left(2x-3\right)=0\)

\(\Leftrightarrow\left(x-9\right)^2\cdot\left(2x-3\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}\left(x-9\right)^2=0\\2x-3=0\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=9\\x=\dfrac{3}{2}\end{matrix}\right.\)

Vậy \(x_1=\dfrac{3}{2};x_2=9\)