Solve 5.4^x+1 - 16^x = 64

5.4^{x + 1} - 16^x = 64
or, 5.4^x.4 - 4^2x = 64

Let 4^x = a

or, 20a - a² = 64
or, a² - 20a + 64 = 0
or, a² - (16 + 4)a + 64 = 0
or, a² - 16a - 4a + 64 = 0
or, a(a - 16) -4(a - 16) = 0
or, (a - 16)(a - 4) = 0

Either, a = 16
so, 4^x = 4²
so, x = 2

OR, a = 4
so, 4^x = 4
so, x = 1

Hence, x = 1, 2