Answer
$7g(3g-8)(2g+5)$
Work Step by Step
First factor out the greatest common factor $7g$:
$42g^3-7g^2-280g=7g(6g^2-g-40)$
Rewrite the middle term and group terms:
$7g(6g^2-16g+15g-40)=7g[2g(3g-8)+5(3g-8)]$
Factor out $3g-8$ from each group:
$7g(3g-8)(2g+5)$