Real and non-real roots to a quintic equation

The question is:

Establish that alpha=2+3i is a root of the quintic equation

3z^5 + 2z^4 - 64z^3 +384z^2 - 667z +182 =0

and find the remaining roots.

Now, I know that as it's a quintic there will be five roots. As I'm told that 2+3i is a root, I can know that 2-3i is also a root. And once I get so far I will be able to divide, take the one real root and the other two complex roots.

But I'm falling at the first hurdle, how do I show that 2+3i is a root?