\(\left(x-1\right)^2+\left(x+3\right)^2=\left(x-2\right)\left(x+1\right)+12\)
\(\Leftrightarrow\left(x^2-2x+1\right)+\left(x^2+6x+9\right)=x^2-x-2+12\)
\(\Leftrightarrow2x^2+4x+10=x^2-x+10\)
\(\Leftrightarrow2x^2+4x=x^2-x\)
\(\Leftrightarrow x^2+4x=-x\)
\(\Leftrightarrow x^2+5x=0\)
\(\Leftrightarrow x\left(x+5\right)=0\)
\(\Rightarrow\orbr{\begin{cases}x=0\\x+5=0\end{cases}\Rightarrow\orbr{\begin{cases}x=0\\x=-5\end{cases}}}\)