\[\begin{array}{l}
a,\;x\; - \;3\; = \;{\left( {3\; - \;x} \right)^2}\\
\Leftrightarrow {\left( {x - 3} \right)^2} - \left( {x - 3} \right) = 0\\
\Leftrightarrow \left( {x - 3} \right)\left( {x - 3 - 1} \right) = 0\\
\Leftrightarrow \left( {x - 3} \right)\left( {x - 4} \right) = 0\\
\Leftrightarrow \left[ \begin{array}{l}
x - 3 = 0\\
x - 4 = 0
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x = 3\\
x = 4
\end{array} \right.\\
vay:S = \{ 3;4\} \\
{\rm{ }}b,\;27{x^3}\; - \;54{x^2}\; + \;36x\; = \;8\\
\Leftrightarrow {\left( {3x} \right)^3} - 3.{\left( {3x} \right)^2}.2 + 3.3x{.2^2} - {2^3} = 0\\
\Leftrightarrow {\left( {3x - 2} \right)^3} = 0\\
\Leftrightarrow 3x - 2 = 0\\
\Leftrightarrow x = \frac{2}{3}\\
vay:x = \frac{2}{3}\\
c,\;{x^3} - \;4x\; - 14x.\left( {x\; - \;2} \right)\; = \;0\\
\Leftrightarrow x\left( {{x^2} - 4} \right) - 14x\left( {x - 2} \right) = 0\\
\Leftrightarrow x\left( {x - 2} \right)\left( {x + 2} \right) - 14x\left( {x - 2} \right) = 0\\
\Leftrightarrow \left( {x - 2} \right)\left( {{x^2} + 2x - 14x} \right) = 0\\
\Leftrightarrow \left( {x - 2} \right)\left( {{x^2} - 12x} \right) = 0\\
\Leftrightarrow \left( {x - 2} \right)x\left( {x - 12} \right) = 0\\
\Leftrightarrow \left[ \begin{array}{l}
x - 2 = 0\\
x = 0\\
x - 12 = 0
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x = 2\\
x = 0\\
x = 12
\end{array} \right.\\
Vay:S = \{ 2;0;12\} \\
d,\;9.{\left( {x\; + \;1} \right)^2}\; - \;{\left( {3\; - \;5x} \right)^2}\; = \;0\\
\Leftrightarrow {\left( {3x + 3} \right)^2} - {\left( {3 - 5x} \right)^2} = 0\\
\Leftrightarrow \left( {3x + 3 - 3 + 5x} \right)\left( {3x + 3 + 3 - 5x} \right) = 0\\
\Leftrightarrow 8x\left( {6 - 2x} \right) = 0\\
\Leftrightarrow \left[ \begin{array}{l}
8x = 0\\
6 - 2x = 0
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x = 0\\
x = 3
\end{array} \right.\\
vay:S = \{ 0;3\}
\end{array}\]