Calculul algebric [ tare urgent ]

{x^2} + 12x = - 32 \Leftrightarrow {x^2} + 12x + 32 = 0 \Leftrightarrow \left( {x + 4} \right)\left( {x + 8} \right) = 0 \Rightarrow \left\{ \begin{gathered}
{x_1} = - 4 \hfill \\
{x_2} = - 8 \hfill \\
\end{gathered} \right.

\begin{gathered}
25{(x + 3)^2} - 36 \Leftrightarrow {5^2}{(x + 3)^2} - {6^2} = {(5x + 15)^2} - {6^2} = \left( {5x + 15 - 6} \right)\left( {5x + 15 + 6} \right) \hfill \\
= \left( {5x + 9} \right)\left( {5x + 21} \right) \hfill \\
\end{gathered}

{x^2} + x - 2 = {x^2} - 1 + x - 1 = \left( {x - 1} \right)\left( {x + 1} \right) + x - 1 = \left( {x - 1} \right)\left( {x + 2} \right)

\begin{gathered}
{\left( {5x - 3} \right)^2} - {\left( {3x - 4} \right)^2} = 25{x^2} - 30x + 9 - \left( {9{x^2} - 24x + 16} \right) = 16{x^2} - 6x - 7 \hfill \\
16{x^2} - 6x - 7 = \left( {2x + 1} \right)\left( {8x - 7} \right) \hfill \\
\end{gathered}