Solve 4^x - 6.2^x+1 + 32 = 0

You just need to separate the 2^x and substitute its value for some variable. And then substitute it back to the original value.

4^x - 6.2^{x + 1} + 32 = 0
or, 4^x - 6.2^x.2 + 32 = 0
or, 2^2x - 6.2^x.2 + 32 = 0

Let 2^x = a

or, a² - 6.a.2 + 32 = 0
or, a² - (8 + 4)a + 32 = 0
or, a² - 8a - 4a + 32 = 0
or, a(a - 8) - 4(a - 8) = 0
or, (a - 8)(a - 4) = 0

Either a = 8
so, 2^x = 2³
so, x = 3

OR, a = 4
so, 2^x = 2²
∴ x = 2

Hence, x = 2, 3

Video explanation: