Regression plane coefficients

I apologize in advance if this question is too simple, but I am new to the topic. I am trying to calculate the regression plane coefficients for a vector of 3D points. So far I have been able to calculate A and B in the general plane equation:

z=Ax +By +C

What do I do to calculate C? Everywhere I have seen they all just say

C=z-Ax-By

but since I have a vector of 3D points, how can I use this formula for the calculation of the third coefficient?