e^4-5e^2+4=0

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Solution for e^4-5e^2+4=0 equation: 


Simplifying
e4 + -5e2 + 4 = 0

Reorder the terms:
4 + -5e2 + e4 = 0

Solving
4 + -5e2 + e4 = 0

Solving for variable 'e'.

Factor a trinomial.
(1 + -1e2)(4 + -1e2) = 0

Factor a difference between two squares.
((1 + e)(1 + -1e))(4 + -1e2) = 0

Factor a difference between two squares.
((2 + e)(2 + -1e))(1 + e)(1 + -1e) = 0


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

Simplifying
1 + e = 0

Solving
1 + e = 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 + e = 0 + -1

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

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

Simplifying
e = -1

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

Simplifying
1 + -1e = 0

Solving
1 + -1e = 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 + -1e = 0 + -1

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

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

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

Simplifying
e = 1

Subproblem 3
Set the factor '(2 + e)' equal to zero and attempt to solve:

Simplifying
2 + e = 0

Solving
2 + e = 0

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

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

Combine like terms: 2 + -2 = 0
0 + e = 0 + -2
e = 0 + -2

Combine like terms: 0 + -2 = -2
e = -2

Simplifying
e = -2

Subproblem 4
Set the factor '(2 + -1e)' equal to zero and attempt to solve:

Simplifying
2 + -1e = 0

Solving
2 + -1e = 0

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

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

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

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

Divide each side by '-1'.
e = 2

Simplifying
e = 2
Solution
e = {-1, 1, -2, 2}

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