1, \(5x\left(x-1\right)=x-1\Rightarrow5x\left(x-1\right)-\left(x-1\right)=0\)
\(\Rightarrow\left(x-1\right)\left(5x-1\right)=0\Rightarrow\orbr{\begin{cases}x-1=0\\5x-1=0\end{cases}\Rightarrow\orbr{\begin{cases}x=1\\x=\frac{1}{5}\end{cases}}}\)
2, \(2x\left(12x-5\right)-8x\left(3x-1\right)=30\)
\(\Rightarrow24x^2-10x-24x^2+8x=30\) \(\Rightarrow-2x=30\Rightarrow x=-15\)
3, \(3x\left(3-2x\right)+6x\left(x-1\right)=15\) \(\Rightarrow9x-6x^2+6x^2-6x=15\Rightarrow3x=15\Rightarrow x=5\)
4, \(x\left(x-3\right)+x-3=0\Rightarrow\left(x-3\right)\left(x+1\right)=0\)
\(\Rightarrow\orbr{\begin{cases}x-3=0\\x+1=0\end{cases}\Rightarrow\orbr{\begin{cases}x=3\\x=-1\end{cases}}}\)
