e^4-4e^2+3=0

Solution for e^4-4e^2+3=0 equation:

Simplifying
e4 + -4e2 + 3 = 0

Reorder the terms:
3 + -4e2 + e4 = 0

Solving
3 + -4e2 + e4 = 0

Solving for variable 'e'.

Factor a trinomial.
(1 + -1e2)(3 + -1e2) = 0

Factor a difference between two squares.
((1 + e)(1 + -1e))(3 + -1e2) = 0

Subproblem 1
Set the factor '(3 + -1e2)' equal to zero and attempt to solve:

Simplifying
3 + -1e2 = 0

Solving
3 + -1e2 = 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 + -1e2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1e2 = 0 + -3
-1e2 = 0 + -3

Combine like terms: 0 + -3 = -3
-1e2 = -3

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

Simplifying
e2 = 3

Take the square root of each side:
e = {-1.732050808, 1.732050808}
Subproblem 2
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 3
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
Solution
e = {-1.732050808, 1.732050808, -1, 1}