Stuck on proof by induction

Hey, Stuck on this proof by induction question. I can get so far but not sure where to go after.

$\displaystyle 3*2^n < n!$ when $\displaystyle n>4$

Basis for Induction

$\displaystyle 3*2^5 < 5!$

$\displaystyle 96 < 120$

Induction Step

We assume $\displaystyle 3*2^n <n!$ when $\displaystyle n>4$

We need to prove that $\displaystyle 3*2^n^+^1 < (n+1)!$

$\displaystyle (n+1)! = (n+1)n!$

$\displaystyle (3*2^n)(n+1)<(n+1)n!$

$\displaystyle (3*2^n)(n+1)<(n+1)!$

This is as far as I can get :( Any help would be appreciated!