Well, you might want to do that, but if both w and d are unknowns, then even if you do it with pencil and paper, you won't succeed.
You would be closer if you had asked to solve for the form w^2/d than w*d^2, but even that will fail. Note that w appears only as w^2. And only one of those terms is divided by d. So, first factor out w^2.
G = w^2*(f_1*L/d + C/2)
You can trivially solve for w^2.
w^2 = G/(f_1*L/d + C/2)
In fact, you can trivially solve for w, by taking the square root as long as you are willing to choose which branch of the square root applies.
But nothing will allow you to get that expression in the form w/d^2, with no d terms on the right hand side. Wanting magic to happen is not sufficient. No symbolic computational engine will do the mathematically impossible either.
