\(\begin{array}{l}
a)\,\,{x^2} - x - 6 = 0\\
\Leftrightarrow {x^2} + 2x - 3x - 6 = 0\\
\Leftrightarrow x\left( {x + 2} \right) - 3\left( {x + 2} \right) = 0\\
\Leftrightarrow \left( {x + 2} \right)\left( {x - 3} \right) = 0\\
\Leftrightarrow \left[ \begin{array}{l}
x + 2 = 0\\
x - 3 = 0
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
x = - 2\\
x = 3
\end{array} \right.\\
Vay\,\,S = \left\{ { - 2;3} \right\}\\
b)\,\,{x^2} - 4x - 12 = 0\\
\Leftrightarrow {x^2} + 2x - 6x - 12 = 0\\
\Leftrightarrow x\left( {x + 2} \right) - 6\left( {x + 2} \right) = 0\\
\Leftrightarrow \left( {x + 2} \right)\left( {x - 6} \right) = 0\\
\Leftrightarrow \left[ \begin{array}{l}
x + 2 = 0\\
x - 6 = 0
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
x = - 2\\
x = 6
\end{array} \right.\\
Vay\,\,S = \left\{ { - 2;6} \right\}\\
c)\,\,\left( {x + 2} \right)\left( {2x - 1} \right) + 1 = 4{x^2}\\
\Leftrightarrow 2{x^2} - x + 4x - 2 + 1 - 4{x^2} = 0\\
\Leftrightarrow - 2{x^2} + 3x - 1 = 0\\
\Leftrightarrow 2{x^2} - 3x + 1 = 0\\
\Leftrightarrow 2{x^2} - 2x - x + 1 = 0\\
\Leftrightarrow 2x\left( {x - 1} \right) - \left( {x - 1} \right) = 0\\
\Leftrightarrow \left( {x - 1} \right)\left( {2x - 1} \right) = 0\\
\Leftrightarrow \left[ \begin{array}{l}
x - 1 = 0\\
2x - 1 = 0
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
x = 1\\
x = \dfrac{1}{2}
\end{array} \right.\\
Vay\,\,S = \left\{ {1;\dfrac{1}{2}} \right\}
\end{array}\)
