\(\left(2x+3\right)^2+\left(x-1\right)^2=10\)
\(\Leftrightarrow4x^2+12x+9+x^2-2x+1-10=0\)
\(\Leftrightarrow5x^2+10x=0\)
\(\Leftrightarrow5x\left(x+2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}5x=0\\x+2=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=-2\end{matrix}\right.\)
Vậy \(S=\left\{-2;0\right\}\)