Let P(z)=z^{3}+a z^{2}+b z+c, where a, b, and c are real. There exists a complex number w such

that the three roots of P(z) are w+3 i, w+9 i, and 2 w-4, where i^{2}=-1. Find |a+b+c|.

that the three roots of P(z) are w+3 i, w+9 i, and 2 w-4, where i^{2}=-1. Find |a+b+c|.