Answer
$w(3w-2)(w^{2}+6)$
Work Step by Step
$3w^{4}-2w^{3}+18w^{2}-12w=$
...factor out the GCF.
$=w(3w^{3}-2w^{2}+18w-12)$
...factor by grouping the first term with the third,
and the second term with the last.
$=w[3w(w^{2}+6)-2(w^{2}+6)]$
...factor again.
$=w(3w-2)(w^{2}+6)$
