\(a,\left(6-9x\right)^2=\left(5x-7\right)^2\Leftrightarrow\left|6-9x\right|=\left|5x-7\right|\\ \Leftrightarrow\left[{}\begin{matrix}6-9x=5x-7\\6-9x=-\left(5x-7\right)\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}14x=13\\4x=-1\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=\dfrac{13}{14}\\x=-\dfrac{1}{4}\end{matrix}\right.\)
\(b,\left(1+x\right)^2=\left(x-1\right)^2\Leftrightarrow\left|1+x\right|=\left|x-1\right|\)
\(\Leftrightarrow\left[{}\begin{matrix}x+1=x-1\\x+1=-\left(x-1\right)\end{matrix}\right.\)\(\Leftrightarrow x=0\).
\(c,\left(3x+1\right)^2-4\left(x-3\right)^2=0\Leftrightarrow\left(3x+1\right)^2=[2\left(x-3\right)]^2\)
\(\Leftrightarrow\left|3x+1\right|=\left|2\left(x-3\right)\right|\Leftrightarrow\left[{}\begin{matrix}3x+1=2\left(x-3\right)\\3x+1=-2\left(x-3\right)\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-7\\x=1\end{matrix}\right.\)
