`3x(x-1)+x-1=0`
`<=>(x-1)(3x+1)=0`
`<=>[(x-1=0),(3x+1=0):}`
`<=>[(x=1),(x=-1/3):}`
\(< =>3x\left(x-1\right)+\left(x-1\right)=0< =>\left(3x+1\right)\left(x-1\right)=0< =>\left\{{}\begin{matrix}3x+1=0\\x-1=0\end{matrix}\right.< =>\left\{{}\begin{matrix}x=-\dfrac{1}{3}\\1\end{matrix}\right.\)