a) \(\left(x+2\right)^2-\left(x+4\right)^2=0\)
\(\Rightarrow\left(x+2-x-4\right)\left(x+2+x+4\right)=0\)
\(\Rightarrow\left(-2\right)\left(2x+6\right)=0\)
\(\Rightarrow\left(-2\right).2.\left(x+3\right)=0\)
\(\Rightarrow x+3=0\) (vì \(-4\ne0\) )
\(\Rightarrow x=-3\)
Vậy \(x=-3\) (câu này mk có sửa đề ko biết có đúng ko 
!!!)
b) \(\left(x-3\right)^2-9=0\Rightarrow\left(x-3\right)^2=9\)
\(\Rightarrow\left[{}\begin{matrix}\left(x-3\right)^2=3^2\\\left(x-3\right)^2=\left(-3\right)^2\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x-3=3\\x-3=-3\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=6\\x=0\end{matrix}\right.\)
Vậy \(x=6\) hoặc \(x=0\)
c) \(x^2+6x+9=0\Rightarrow\left(x+3\right)^2=0\)
\(\Rightarrow x+3=0\Rightarrow x=-3\)
Vậy \(x=-3\)
d) \(-x^3+9x^2-27x+27=0\)
\(\Rightarrow-\left(x^3-9x^2+27x-27\right)=0\)
\(\Rightarrow-\left(x-3\right)^3=0\)
\(\Rightarrow x-3=0\)
\(\Rightarrow x=3\)
Vậy \(x=3\)