4^x - 5 x 2^x +4 = 0 ( let u = 2^x )

4^x - 5*2^x + 4 = 0

Replace 2^x by u so the above becomes:

u² - 5u + 4 = 0   because 4^x = (2*2)^x = 2^x*2^x = u²

This factorizes nicely into:

(u - 1)*(u - 4) = 0

so u = 1 and u = 4

so 2^x = 1 and 2^x = 4 which means that the two values for x are x = 0 and x = 2

Is the $${\mathtt{u}}$$ in the question? The only variable in the question is $${\mathtt{x}}$$, not $${\mathtt{u}}$$.