2e^4x-e^2x=

Solution for 2e^4x-e^2x= equation:

Simplifying
2e4x + -1e2x = 0

Reorder the terms:
-1e2x + 2e4x = 0

Solving
-1e2x + 2e4x = 0

Solving for variable 'e'.

Factor out the Greatest Common Factor (GCF), 'e2x'.
e2x(-1 + 2e2) = 0

Subproblem 1
Set the factor 'e2x' equal to zero and attempt to solve:

Simplifying
e2x = 0

Solving
e2x = 0

Move all terms containing e to the left, all other terms to the right.

Simplifying
e2x = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(-1 + 2e2)' equal to zero and attempt to solve:

Simplifying
-1 + 2e2 = 0

Solving
-1 + 2e2 = 0

Move all terms containing e to the left, all other terms to the right.

Add '1' to each side of the equation.
-1 + 1 + 2e2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 2e2 = 0 + 1
2e2 = 0 + 1

Combine like terms: 0 + 1 = 1
2e2 = 1

Divide each side by '2'.
e2 = 0.5

Simplifying
e2 = 0.5

Take the square root of each side:
e = {-0.707106781, 0.707106781}
Solution
e = {-0.707106781, 0.707106781}