\(\begin{array}{l}
a)\,\,x\left( {2x - 1} \right) - \left( {x - 2} \right)\left( {2x + 3} \right) = 0\\
\Leftrightarrow 2{x^2} - x - \left( {2{x^2} + 3x - 4x - 6} \right) = 0\\
\Leftrightarrow 2{x^2} - x - 2{x^2} - 3x + 4x + 6 = 0\\
\Leftrightarrow 6 = 0\,\,\left( {vo\,\,ly} \right)\\
b)\,\,\left( {x - 1} \right)\left( {x + 2} \right) - x - 2 = 0\\
\Leftrightarrow \,\left( {x - 1} \right)\left( {x + 2} \right) - \left( {x + 2} \right) = 0\\
\, \Leftrightarrow \left( {x + 2} \right)\left( {x - 1 - 1} \right) = 0\\
\Leftrightarrow \left( {x + 2} \right)\left( {x - 2} \right) = 0\\
\Leftrightarrow \left[ \begin{array}{l}
x + 2 = 0\\
x - 2 = 0
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
x = - 2\\
x = 2
\end{array} \right.
\end{array}\)
