\(x\left(x-10\right)+x-10=0\)
\(\Leftrightarrow x\left(x-10\right)+1\left(x-10\right)=0\)
\(\Leftrightarrow\left(x-10\right)\left(x+1\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x-10=0\\x+1=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=10\\x=-1\end{cases}}\)