\(7+\left(3x+2\right)^2=71\\ \Leftrightarrow7+9x^2+12x+4=71\\ \Leftrightarrow11+9x^2+12x=71\\ \Leftrightarrow11+9x^2+12x-71=0\\ \Leftrightarrow9x^2+12x-60=0\\ \Leftrightarrow3x^2+4x-20=0\\ \Leftrightarrow3x^2+10x-6x-20=0\\ \Leftrightarrow x\left(3x+10\right)-2\left(3x+10\right)=0\\ \Leftrightarrow\left(3x+10\right)\left(x-2\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}3x+10=0\\x-2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}3x=-10\\x=2\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{10}{3}\\x=2\end{matrix}\right.\)
Vậy tập nghiệm phương trình là \(S=\left\{-\dfrac{10}{3};2\right\}\)
