Find the value of x in 4 • 4^x-2 + 2^2x-2 = (1/32)^2x+5

The answer is x=-2

I'd like the steps of it since I already have the answer

Thanks!

4 • 4^x-2 + 2^2x-2 = (1/32)^2x+5
4^(x-1) + 2^(2x-2) = (1/2^5)^(2x+5)
2^(2x-2) + 2^(2x-2) = (1/2)^(10x+25)
2 * 2^(2x-2) = 2^(-10x-25)
2^(2x-1) = 2^(-10x-25)

equating powers:
2x-1 = -10x-25
12x = -24
x = -2

4 * 4^(x - 2) + 2^(2x - 2) = (1/32)^(2x + 5)
4 * (2^2)^(x - 2) + 2^(2x - 2) = (2^(-5))^(2x + 5)
4 * 2^(2 * (x - 2)) + 2^(2x - 2) = 2^(-5 * (2x + 5))
4 * 2^(2x - 4) + 2^(2x - 2) = 2^(-10x - 25)
4 * 2^(2x) / 2^4 + 2^(2x) / 2^2 = 2^(-10x - 25)
4 * 2^(2x) / 16 + 2^(2x) / 4 = 2^(-10x - 25)
2^(2x) / 4 + 2^(2x) / 4 = 2^(-10x - 25)
2 * 2^(2x) / 4 = 2^(-10x - 25)
2^(2x) / 2 = 2^(-10x - 25)
2^(2x - 1) = 2^(-10x - 25)
2x - 1 = -10x - 25
2x + 10x = -25 + 1
12x = -24
x = -2