2e^2x=e^2

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

Simplifying
2e2x = e2

Solving
2e2x = e2

Solving for variable 'e'.

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

Add '-1e2' to each side of the equation.
-1e2 + 2e2x = e2 + -1e2

Combine like terms: e2 + -1e2 = 0
-1e2 + 2e2x = 0

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

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 '(-1 + 2x)' equal to zero and attempt to solve:

Simplifying
-1 + 2x = 0

Solving
-1 + 2x = 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 + 2x = 0 + 1

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

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

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

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

Simplifying
0 = 1 + -2x

The solution to this equation could not be determined.

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