a) \(3\left(x-2\right)^2+9\left(x-1\right)=3\left(x^2+x-3\right)\\ \Leftrightarrow3\left(x^2-4x+4\right)+9x-9=3x^2+3x-9\\ \Leftrightarrow3x^2-3x^2-12x+9x-3x=-12+9-9\\ \Leftrightarrow-6x=-12\\ \Leftrightarrow x=2\\ \Rightarrow S=\left\{2\right\}\)
b) \(\left(x+3\right)^2-\left(x-3\right)^2=6x+16\\ \Leftrightarrow\left(x^2+6x+9\right)-\left(x^2-6x+9\right)-6x-16=0\\ \Leftrightarrow6x=16\\ \Leftrightarrow x=\frac{8}{3}\\ \Rightarrow S=\left\{\frac{8}{3}\right\}\)