2e^4x=6e^2

Solution for 2e^4x=6e^2 equation:

Simplifying
2e4x = 6e2

Solving
2e4x = 6e2

Solving for variable 'e'.

Reorder the terms:
-6e2 + 2e4x = 6e2 + -6e2

Combine like terms: 6e2 + -6e2 = 0
-6e2 + 2e4x = 0

Factor out the Greatest Common Factor (GCF), '2e2'.
2e2(-3 + e2x) = 0

Ignore the factor 2.
Subproblem 1
Set the factor 'e2' equal to zero and attempt to solve:

Simplifying
e2 = 0

Solving
e2 = 0

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

Simplifying
e2 = 0

Take the square root of each side:
e = {0}
Subproblem 2
Set the factor '(-3 + e2x)' equal to zero and attempt to solve:

Simplifying
-3 + e2x = 0

Solving
-3 + e2x = 0

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

Add '3' to each side of the equation.
-3 + 3 + e2x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + e2x = 0 + 3
e2x = 0 + 3

Combine like terms: 0 + 3 = 3
e2x = 3

Divide each side by 'x'.
e2 = 3x-1

Simplifying
e2 = 3x-1

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
e = {0}