When you were trying to multply through in the common denominator step, -132E-33I3(330R) - 20I3(200R) -20E = I3
it looks like you are multplying twice? I don't understand what you are doing there. Also, your denominator isn't correct, what does R*R give you? Be very careful with your signs.
It would help to see the entire problem, especially since I didn't get the same answer as your instructor. Maybe you haven't set up the equation properly?