In case you care about the maths, it works like this: Remember that in ax + by + cz + d = 0, a, b and c are the three components of the normal vector of the plane, while d is -N*P0 - that's the dot product of the normal vector with the point on the plane. In other words, this formula represents the plane as represented by a point and a normal.

To get from three points to this representation, you choose any of the three points p1, p2 and p3 to be your p0. Then you need to compute the normal. For this, you calculate v2 and v3 as the vectors from p1 to p2 and p3, respectively. Then, you do a cross product on these two to get the normal.

Finally, you just fill in the values.