\(\left(3x+1\right)^2-4\cdot\left(x-3\right)^2=0\)
\(\left(3x+1\right)^2-\left(2x-6\right)^2=0\)
\(\left(3x+1-2x+6\right)\left(3x+1+2x-6\right)=0\)
\(\left(x+7\right)\left(5x-5\right)=0\)
\(\left[{}\begin{matrix}x+7=0\\5x-5=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=-7\\x=1\end{matrix}\right.\)