Interesting Math Olympiad Problem || Hardest Algebra Problem in the World || Math Olympiad || 

Again a drastically overcomplicated road to Rome: At (0:40) he already anticipated the solution and directly had it standing at that line before his eyes. Without anticipating the solution, the reforming step would have had no sense at all. With anticipation, if you at this point do not grasp the solution at first glance, you could factor out 9 from the constants and n^2 from the powers. Then at least the solution is directly spitting into your face. It's easier to spot if the constants remain on the RHS. Of course, with all those reformation (even the simple initial ones), we assume the value space being restricted to Z+, which should be stated at the problem presentation. OK, he did take the complex plane into account. Thus, after finding the initial solution, you can just divide the equation by (x-3), which yields the equation at (3:50). From that point on, the rest is necessary for finding the remaining solutions.