Factor polynomial $$ -6mp+4m+18p-12 $$

$$ -6mp+4m+18p-12 = -2(m-3)(3p-2) $$

Step 1 :

Factor out common factor $ \color{blue}{ -2 } $:

$$ -6mp+4m+18p-12 = -2 ( 3mp-2m-9p+6 ) $$

Step 2 :

To factor $ 3mp-2m-9p+6 $ we can use factoring by grouping.

Group $ \color{blue}{ 3mp }$ with $ \color{blue}{ -2m }$ and $ \color{red}{ -9p }$ with $ \color{red}{ 6 }$ then factor each group.

$$ \begin{aligned} 3mp-2m-9p+6 &= ( \color{blue}{ 3mp-2m } ) + ( \color{red}{ -9p+6 }) = \\ &= \color{blue}{ m( 3p-2 )} \color{red}{ -3( 3p-2 ) } = \\ &= (m-3)(3p-2) \end{aligned} $$

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