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

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

Simplifying
n4 + -4n2 + 3 = 0

Reorder the terms:
3 + -4n2 + n4 = 0

Solving
3 + -4n2 + n4 = 0

Solving for variable 'n'.

Factor a trinomial.
(1 + -1n2)(3 + -1n2) = 0

Factor a difference between two squares.
((1 + n)(1 + -1n))(3 + -1n2) = 0

Subproblem 1
Set the factor '(3 + -1n2)' equal to zero and attempt to solve:

Simplifying
3 + -1n2 = 0

Solving
3 + -1n2 = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1n2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1n2 = 0 + -3
-1n2 = 0 + -3

Combine like terms: 0 + -3 = -3
-1n2 = -3

Divide each side by '-1'.
n2 = 3

Simplifying
n2 = 3

Take the square root of each side:
n = {-1.732050808, 1.732050808}
Subproblem 2
Set the factor '(1 + n)' equal to zero and attempt to solve:

Simplifying
1 + n = 0

Solving
1 + n = 0

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

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

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

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

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

Simplifying
1 + -1n = 0

Solving
1 + -1n = 0

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

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

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

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

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

Simplifying
n = 1
Solution
n = {-1.732050808, 1.732050808, -1, 1}