How have yo got 32^x = 3*2^x. In fact 32^x= (2^5)^x = 2^5x

secondly what you are thinking about ( sqrt4)^x = 2^x is absolutely correct.

please check the question once again if it has been correctly written, in present form we get

2^x[ x^2 - 4x - 2^(4x) ]=0