e^4=x^4

Solution for e^4=x^4 equation:

Simplifying
e4 = x4

Solving
e4 = x4

Solving for variable 'e'.

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

Simplifying
e4 = x4

Combine like terms: x4 + -1x4 = 0
e4 + -1x4 = 0

Factor a difference between two squares.
(e2 + x2)(e2 + -1x2) = 0

Factor a difference between two squares.
(e2 + x2)((e + x)(e + -1x)) = 0

Subproblem 1
Set the factor '(e2 + x2)' equal to zero and attempt to solve:

Simplifying
e2 + x2 = 0

Solving
e2 + x2 = 0

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

Add '-1x2' to each side of the equation.
e2 + x2 + -1x2 = 0 + -1x2

Combine like terms: x2 + -1x2 = 0
e2 + 0 = 0 + -1x2
e2 = 0 + -1x2
Remove the zero:
e2 = -1x2

Simplifying
e2 = -1x2

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 '(e + x)' equal to zero and attempt to solve:

Simplifying
e + x = 0

Solving
e + x = 0

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

Add '-1x' to each side of the equation.
e + x + -1x = 0 + -1x

Combine like terms: x + -1x = 0
e + 0 = 0 + -1x
e = 0 + -1x
Remove the zero:
e = -1x

Simplifying
e = -1x
Subproblem 3
Set the factor '(e + -1x)' equal to zero and attempt to solve:

Simplifying
e + -1x = 0

Solving
e + -1x = 0

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

Add 'x' to each side of the equation.
e + -1x + x = 0 + x

Combine like terms: -1x + x = 0
e + 0 = 0 + x
e = 0 + x
Remove the zero:
e = x

Simplifying
e = x
Solution
e = {-1x, x}