All numbers are assumed nonzero natural numbers. All numbers are assumed unequal.
Suppose we have $ab = xy$, and $a+b = cd$.
$x$ is set to be fixed from beginning, and it is assumed that one knows the prime factorization of it. $d$ is not fixed, and $d$ is a factor of $x$.
What I want to know is how one finds/sets the values of $a,b,c,d,y$ that satisfies the constraint with the given $x$.
Edit: I edited the question so that $d$ is now a factor of $x$.
Without brute-forcing, what would be an easy way to find a possible way of setting values?