Concavity and Points of Inflection!

Have a few questions guys

**1. Test $\displaystyle f(x)=5x^4-9x^3+3$ for concavity and inflection points. **

**So, to find the inflection points, I know I need to apply the 2nd derivative test which I got: $\displaystyle f(x)=60x^2-54x$

From here, I set the 2nd derivative =0 which I am having a hard time with.... I think I need to factor somewhere but I don't see it (well its not obvious to me hence I am here. ) For Concavity, you just plug in numbers that are bigger or smaller than your critical # to find where its concavity correct?

*And can someone help me with the concavity question?*

The Second question:

**2. Test the function $\displaystyle 6x^3-(108)x^2+(630)x-2$ for relative maximum and minimum.**

** I applied the second derivative test again to try and find the critical points: f''(x)=24x-216

Which my textbook tells me is wrong.

As usual, TIA