"Reduce" an expression in terms of a sub-expression

Question

Newbie here. I've been trying to use Reduce to solve a rather long equation. The evaluation has been running for more than hour now, but still hasn't stopped. I've got an inkling that if I were to just "Reduce" it in terms of not a single variable, but an sub-expression in the equation, it might be shorter for Mathematica to reduce.

random example:

bm - am - pn(p(b - a) + pb - pbm - pa + pa*m) = 5b

I want to put (b - a) on one side, regardless whether it will eliminate all "b" and "a" on the other side:

5b/(m - pn(2p - pm)) = (b - a)

As you can see, "b" as "5b" is still on the other side, but still I'd like to ask Mathematica ATTEMPT to reduce it like this. Is there a built-in function for this?

Of course, if all "a" and "b", mathematically, cannot be on just one side, the form might vary vastly and the user might have to find a way to work with that. But, if it is mathematically possible, then Mathematica should be able to reduce it at least most of the time.

Answer 1

b m - a m - p n (p (b - a) + p b - p b m - p a + p a m) == 5 b

FullSimplify@Solve[% /. a -> b - x, x][[1]] /. Rule -> Equal /. x -> b - a

{-a + b == (5 b)/(m + (-2 + m) n p^2)}