Question 7Let $P(z) = z^3 + az^2 + bz + c,$ 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 $|a + b + c|.$