Question 617384
Notice how 4 and 32 are powers of 2. So rewrite them as such and simplify...



4^(2x-1) = 32^(x+2)


(2^2)^(2x-1) = (2^5)^(x+2)


2^(2(2x-1)) = 2^(5(x+2))



Since the bases are equal (to 2), the exponents must be equal. So....


2(2x-1) = 5(x+2)


4x-2 = 5x+10


4x-5x = 10+2


-x = 12


x = -12


So the solution is <font color="red">x = -12</font>