Factor polynomial $$ 6ax^{2}-9ax-4cx+6c $$

$$ 6ax^{2}-9ax-4cx+6c = (3ax-2c)(2x-3) $$

To factor $ 6ax^2-9ax-4cx+6c $ we can use factoring by grouping.

Group $ \color{blue}{ 6ax^2 }$ with $ \color{blue}{ -9ax }$ and $ \color{red}{ -4cx }$ with $ \color{red}{ 6c }$ then factor each group.

$$ \begin{aligned} 6ax^2-9ax-4cx+6c &= ( \color{blue}{ 6ax^2-9ax } ) + ( \color{red}{ -4cx+6c }) = \\ &= \color{blue}{ 3ax( 2x-3 )} \color{red}{ -2c( 2x-3 ) } = \\ &= (3ax-2c)(2x-3) \end{aligned} $$

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