\[\begin{array}{l}
e)4x\left( {x + 2} \right) - {x^2} + 4 = 0\\
\Leftrightarrow 4x\left( {x + 2} \right) - \left( {{x^2} - 4} \right) = 0\\
\Leftrightarrow 4x\left( {x + 2} \right) - \left( {x - 2} \right)\left( {x + 2} \right) = 0\\
\Leftrightarrow \left( {x + 2} \right)\left( {4x - x + 2} \right) = 0\\
\Leftrightarrow \left( {x + 2} \right)\left( {3x + 2} \right) = 0\\
\Leftrightarrow \left[ \begin{array}{l}
x + 2 = 0\\
3x + 2 = 0
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x = - 2\\
x = \frac{{ - 2}}{3}
\end{array} \right.\\
Vay:S = \{ - 2;\frac{{ - 2}}{3}\} \\
f){x^3} - 3{x^2} + x - 3 = 0\\
\Leftrightarrow {x^2}\left( {x - 3} \right) + \left( {x - 3} \right) = 0\\
\Leftrightarrow \left( {x - 3} \right)\left( {{x^2} + 1} \right) = 0\\
\Leftrightarrow x - 3 = 0\left( {do:{x^2} + 1 > 0} \right)\\
\Leftrightarrow x = 3\\
vay:x = 3\\
i){x^2}\left( {2x - 1} \right) = 6x - 3\\
\Leftrightarrow {x^2}\left( {2x - 1} \right) - 3\left( {2x - 1} \right) = 0\\
\Leftrightarrow \left( {2x - 1} \right)\left( {{x^2} - 3} \right) = 0\\
\Leftrightarrow \left[ \begin{array}{l}
2x - 1 = 0\\
{x^2} - 3 = 0
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x = \frac{1}{2}\\
x = \sqrt 3 \\
x = - \sqrt 3
\end{array} \right.\\
vay:S = \{ \frac{1}{2};\sqrt 3 ; - \sqrt 3 \} \\
k)2{x^3} + 6{x^2} = {x^2} + 3x\\
\Leftrightarrow 2{x^2}\left( {x + 3} \right) - x\left( {x + 3} \right) = 0\\
\Leftrightarrow x\left( {x + 3} \right)\left( {2x - 1} \right) = 0\\
\Leftrightarrow \left[ \begin{array}{l}
x = 0\\
x + 3 = 0\\
2x - 1 = 0
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x = 0\\
x = - 3\\
x = \frac{1}{2}
\end{array} \right.\\
vay:S = \{ 0; - 3;\frac{1}{2}\} \\
m)\left( {x - 2} \right)\left( {{x^2} + 3x - 2} \right) - {x^3} = - 8\\
\Leftrightarrow \left( {x - 2} \right)\left( {{x^2} + 3x - 2} \right) - {x^3} + 8 = 0\\
\Leftrightarrow \left( {x - 2} \right)\left( {{x^2} + 3x - 2} \right) - \left( {x - 2} \right)\left( {{x^2} + 2x + 4} \right) = 0\\
\Leftrightarrow \left( {x - 2} \right)\left( {{x^2} + 3x - 2 - {x^2} - 2x - 4} \right) = 0\\
\Leftrightarrow \left( {x - 2} \right)\left( {x - 6} \right) = 0\\
\Leftrightarrow \left[ \begin{array}{l}
x - 2 = 0\\
x - 6 = 0
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x = 2\\
x = 6
\end{array} \right.\\
vay:S = \{ 2;6\} \\
n){x^3} + 27 + \left( {x + 3} \right)\left( {x - 9} \right) = 0\\
\Leftrightarrow \left( {x + 3} \right)\left( {{x^2} - 3x + 9} \right) + \left( {x + 3} \right)\left( {x - 9} \right) = 0\\
\Leftrightarrow \left( {x + 3} \right)\left( {{x^2} - 3x + 9 + x - 9} \right) = 0\\
\Leftrightarrow \left( {x + 3} \right)\left( {{x^2} - 2x} \right) = 0\\
\Leftrightarrow \left[ \begin{array}{l}
x + 3 = 0\\
{x^2} - 2x = 0
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x = - 3\\
x = 0\\
x = 2
\end{array} \right.\\
vay:S = \{ - 3;0;2\}
\end{array}\]