To factor $ 10ab+15b-2a-3 $ we can use factoring by grouping.
Group $ \color{blue}{ 10ab }$ with $ \color{blue}{ 15b }$ and $ \color{red}{ -2a }$ with $ \color{red}{ -3 }$ then factor each group.
$$ \begin{aligned} 10ab+15b-2a-3 &= ( \color{blue}{ 10ab+15b } ) + ( \color{red}{ -2a-3 }) = \\ &= \color{blue}{ 5b( 2a+3 )} \color{red}{ -1( 2a+3 ) } = \\ &= (5b-1)(2a+3) \end{aligned} $$