10^(2·x) - 10^(x - 1) = 10^(x + 2) - 10
10^x = t
t^2 - 1/10·t = 10^2·t - 10
t^2 - 1/10·t - (10^2·t - 10) = 0
t^2 - 1001·t/10 + 10 = 0
10·t^2 - 1001·t + 100 = 0
risolvo ed ottengo: t = 1/10 ∨ t = 100
10^x = 1/10---> x = -1
10^x = 100---> x = 2
In definitiva:
x = 2 ∨ x = -1