\(7x\left(x-1\right)=x-1\)
\(\Rightarrow7x\left(x-1\right)-\left(x-1\right)=0\)
\(\Rightarrow\left(7x-1\right)\left(x-1\right)=0\)
\(\Rightarrow\left[\begin{matrix}7x-1=0\\x-1=0\end{matrix}\right.\)
\(\Rightarrow\left[\begin{matrix}x=\dfrac{1}{7}\\x=1\end{matrix}\right.\)