To solve this equation, we need to first rewrite it in terms of powers of 2 and 4:

216^x - 32^4x - 1 + 7*4^2x - 1 = 120

Since 16 = 2^4 and 4 = 2^2, we can rewrite the equation as:

22^(4x) - 32^(4x) - 1 + 7(2^2)^(2x) - 1 = 120
22^(4x) - 32^(4x) - 1 + 72^(4x) - 1 = 120
22^(4x) - 32^(4x) + 72^(4x) - 2 = 120
62^(4x) - 2 = 120
6*16^x - 2 = 120

Next, we can isolate the exponential term:

6*16^x = 122
16^x = 122/6
16^x = 61/3

Now, we can rewrite 61/3 as a power of 16:

16^x = 16^(61/3)
x = 61/3

Therefore, the solution to the equation is x = 61/3.