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f_x = y/3(24 - 12x - 4y) = 0

f_y = x/3(24 - 6x - 8y) = 0

I get y = 0 and x = (6-y)/3 for x in the first partial. How am I supposed to proceed? If I plug these into the secon, it gets nasty. Can anyone demonstrate how this is done?

Thank you.