\(x^2-1=\left(x-1\right)\left(2x-3\right)\\ \Leftrightarrow x^2-1-\left(x-1\right)\left(2x-3\right)=0\\ \Leftrightarrow\left(x-1\right)\left(x+1\right)-\left(x-1\right)\left(2x-3\right)=0\\ \Leftrightarrow\left(x-1\right)\left(x+1-2x+3\right)=0\\ \Leftrightarrow\left(x-1\right)\left(4-x\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x-1=0\\4-x=0\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=1\\x=4\end{matrix}\right.\)