AIME 2010b Problem 7

Let $P(z)=z^3+az^2+bz+c$, where $a$, $b$, and $c$ are real. There exists a complex number $w$ such that the three roots of $P(z)$ are $w+3i$, $w+9i$, and $2w-4$, where $i^2=-1$. Find $|a+b+c|$.