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Factorize the expression
$ax ^{ 2 } -4ax-12a$
$a \left ( x - 6 \right ) \left ( x + 2 \right )$
Arrange the expression in the form of factorization..
$\color{#FF6800}{ a } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ a } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 12 } \color{#FF6800}{ a }$
 Tie a common factor 
$\color{#FF6800}{ a } \left ( \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 12 } \right )$
$a \left ( \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 12 } \right )$
 Use the factoring formula, $x^{2} + \left(a+b\right)x + ab = \left(x+a\right)\left(x+b\right)$
$a \left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \right ) \left ( \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 6 } \right )$
$a \left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \right ) \left ( \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 6 } \right )$
 Sort the factors 
$a \left ( \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 6 } \right ) \left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \right )$
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