The equation to be solved is 2^x + 4^x = 0.
First, it showed be observed that the base in both the terms 2^x as well as 4^x is positive. When a positive number is raised to the power of any number, positive or negative, the result is a non-zero positive number.
In the given equation as both 2^x and 4^x are non-zero positive numbers their sum cannot be equal to 0.
The given equation does not have any solution.