Single variable algebra formula - use Solver function?

Is there a reason to use Solver (other than you don't want to do the algebra)? Solver should solve this fairly readily, though, if you want to solve it quickly and repeatedly, I would do the algebra. If I did it right:
A1=A3/A2+A4/(1+A2-g)
A1*(1+A2-g)=A3/A2*(1+A2-g)+A4
A1+A1*A2-A1*g=A3/A2+A3-A3*g/A2+A4
A1+A1*A2-A3/A2-A3-A4=A1*g-A3*g/A2=g*(A1-A3/A2)
(A1+A1*A2-A3/A2-A3-A4)/(A1-A3/A2)=g

Did I do that right?

We would probably need to see your Solver model, but I see no reason why Solver should have any trouble finding any of the variables. You haven't specified where you will put g. If I were setting this up, it would probably look something like:

1) A1=formula as given, using some initial guess for g (you haven't yet specified where you will put g.
2) B1 would probably hold the desired 15 (or whatever your desire input for A1)
3) C1 would be =A1-B1.
4) Solver model would be
a) Set Target Cell: C1
b) to a value of 0
c) by changing: g (whatever cell you choose to put g in)

Does that sound like what your other Solver tutorials have been suggesting?