a) \(\left(x-3\right)^{2022}=\left(x-3\right)^{2023}\)
\(\left(x-3\right)^{2022}\left(x-3-1\right)=0\)
\(\left(x-3\right)^{2022}\left(x-4\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=3\\x=4\end{matrix}\right.\)
b) \(\left(x+1\right)^{2024}+\left(x+1\right)^{2023}=2\)
\(\left[\left(x+1\right)^{2022}-1\right]\left[\left(x+1\right)^{2022}+2\right]=0\)
\(\Leftrightarrow x+1=1\)
\(\Leftrightarrow x=0\)
c) \(\left(x+3\right)^2+\left(x+3\right)=12\)
\(\left[\left(x+3\right)-3\right]\left[\left(x+3\right)+4\right]=0\)
\(x\left(x+7\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=-7\end{matrix}\right.\)