You'll want to think of this as a problem with 3 equations and 3 unknowns.
First, rewrite the initial equation by dividing everything by D:
(A/D)x + (B/D)y + (C/D)z = 1
To make this easier, you can substitute in new variables: A/D = m, B/D = n, and C/D = o. So:
mx + ny + oz = 1
Now, you should put each point into this equation, which will give you 3 new equations:
2m + 0 + 0 = 1
0 + 6n + 0 =1
0 + 0 + 5o = 1
In this case you can solve each directly, otherwise you could use substitution:
m = 1/2, n = 1/6, o = 1/5
Now, put these values in the cleaned up equation:
1/2 x + 1/6 y + 1/5 z = 1
This is in standard form, however you can multiply each term by 30 to remove fractions:
15x + 5y + 6z = 30.
