Answer
$2a(2a-3)(3a+7)$
Work Step by Step
Factor out the greatest common factor, $2a$
$=2a\left(6a^{2}+5a-21\right)$
When factoring $ax^{2}+bx+c$, we search for factors of $ac$ whose sum is $b,$
and, if we find them, we rewrite $bx$ and proceed to factor in groups.
Here, factors of $(6)\times(-21)=-126$ that add to $+5$ are ....$+9$ and $-14.$
$=2a\left(6a^{2}+9a-14a-21\right)$
$=2a\left[ \left(6a^{2}-9a\right)+(14a-21) \right]$
$=2a\left[ 3a(2a-3)+7(2a-3) \right]$
$=2a(2a-3)(3a+7)$
