I cannot make any progress in solving this equation for r, and I am convinced there must be an answer:
n(1 - r)y + m(1 - r)z = c + d
Any assistance will be greatly appreciated!
Thank you Wilmer, I suspected that might be the case.
I have managed to solve the problem using the secant method which solves the problem in about 10 steps - which is fast enough for my purposes and is giving me the correct result.