e^2z=e

Solution for e^2z=e equation:

Simplifying
e2z = e

Solving
e2z = e

Solving for variable 'e'.

Reorder the terms:
-1e + e2z = e + -1e

Combine like terms: e + -1e = 0
-1e + e2z = 0

Factor out the Greatest Common Factor (GCF), 'e'.
e(-1 + ez) = 0

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

Simplifying
e = 0

Solving
e = 0

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

Simplifying
e = 0
Subproblem 2
Set the factor '(-1 + ez)' equal to zero and attempt to solve:

Simplifying
-1 + ez = 0

Solving
-1 + ez = 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 + ez = 0 + 1

Combine like terms: -1 + 1 = 0
0 + ez = 0 + 1
ez = 0 + 1

Combine like terms: 0 + 1 = 1
ez = 1

Divide each side by 'z'.
e = z-1

Simplifying
e = z-1
Solution
e = {0, z-1}