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

b) \(x^2-2x=24\)

\(\Rightarrow x-2x-24=0\)

\(\Rightarrow x^2-6x+4x-24=0\\ \Rightarrow x\left(x-6\right)+4\left(x-6\right)=0\\ \Rightarrow\left(x-6\right)\left(x+4\right)=0\\ \Rightarrow\left[{}\begin{matrix}x-6=0\\x+4=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=6\\x=-4\end{matrix}\right.\)

c) \(\left(2x+1\right)^2+\left(x+3\right)^2-5\left(x-7\right)\left(x+7\right)=0\)

\(\Rightarrow4x^2+4x+1+x^2+6x+9-5x^2+245=0\\ \Rightarrow10x+255=0\\ \Rightarrow x=-25.5\)

d) \(\left(x-3\right)\left(x^2+3x+9\right)+x\left(x+2\right)\left(2-x\right)=1\)

\(\Rightarrow x^3-3^3+x\left(2^2-x^2\right)=1\\ \Rightarrow x^3-27+4x-x^3=1\\ \Rightarrow4x=1+27\\ \Rightarrow x=7\)

e) \(\left(3x-1\right)^2+2\left(x+3\right)^2+11\left(x+1\right)\left(1-x\right)=6\)

\(\Rightarrow9x^2-6x+1+2\left(x^2+6x+9\right)+11\left(1-x^2\right)=6\\ \Rightarrow9x^2-6x+1+2x^2+12x+18+11-11x^2=6\\ \Rightarrow6x+30=6\\ \Rightarrow6x=-24\\ \Rightarrow x=-4\)