Step 1 :

After factoring out $ -3e $ we have:

$$ -30e^{4}-45e^{3}+6e^{2}+9e = -3e ( 10e^{3}+15e^{2}-2e-3 ) $$

Step 2 :

To factor $ 10e^{3}+15e^{2}-2e-3 $ we can use factoring by grouping:

Group $ \color{blue}{ 10x^{3} }$ with $ \color{blue}{ 15x^{2} }$ and $ \color{red}{ -2x }$ with $ \color{red}{ -3 }$ then factor each group.

$$ \begin{aligned} 10e^{3}+15e^{2}-2e-3 = ( \color{blue}{ 10x^{3}+15x^{2} } ) + ( \color{red}{ -2x-3 }) &= \\ &= \color{blue}{ 5x^{2}( 2x+3 )} + \color{red}{ -1( 2x+3 ) } = \\ &= (5x^{2}-1)(2x+3) \end{aligned} $$

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