Think of it like this
d= a*b
e = a*c for some a, b and c.
Then dd + e is equal to abab + a*c.
This can be changed to a(ab*b + c). Thus c is divisible by a.
Poor variable name choosing here though. The c in e = ac isn't the same as our c (dd + e). I mean the equation holds it might just be a bit confusing