\(x^3\left(x-1\right)+\left(x-1\right)\left(x-10\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(x^3+x-10\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(x-2\right)\left(x^2+2x+5\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=1\\x=2\end{matrix}\right.\)