Finding points on a plane

I'm brand new here, so feel free to move this post if need be.

I have a plane defined by its unit normal (A, B, C) and a distance (D). I need to define this plane by three points instead. I know the equation for a plane is Ax+By+Cz=D, and it's easy enough if two of the coefficients are zero (the third coefficient is one and the point is dist along that axis). Is there a reliable formula for finding an x, y and z that satisfies this equation, particularly when A, B and C are all nonzero?