\(3\left(x-1\right)^2-x^2+1=0\)
\(\Leftrightarrow3\left(x-1\right)^2-\left(x^2-1\right)=0\)
\(\Leftrightarrow3\left(x-1\right)^2-\left(x-1\right)\left(x+1\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left[3\left(x-1\right)-\left(x+1\right)\right]=0\)
\(\Leftrightarrow\left(x-1\right)\left(3x-3-x-1\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(2x-4\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x-1=0\\2x-4=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=1\\2x=4\end{cases}\Leftrightarrow}\orbr{\begin{cases}x=1\\x=2\end{cases}}}\)
