3n^4-4n^2=-1

Solution for 3n^4-4n^2=-1 equation:

Simplifying
3n4 + -4n2 = -1

Reorder the terms:
-4n2 + 3n4 = -1

Solving
-4n2 + 3n4 = -1

Solving for variable 'n'.

Reorder the terms:
1 + -4n2 + 3n4 = -1 + 1

Combine like terms: -1 + 1 = 0
1 + -4n2 + 3n4 = 0

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

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

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

Simplifying
1 + -3n2 = 0

Solving
1 + -3n2 = 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 + -3n2 = 0 + -1

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

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

Divide each side by '-3'.
n2 = 0.3333333333

Simplifying
n2 = 0.3333333333

Take the square root of each side:
n = {-0.577350269, 0.577350269}
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 = {-0.577350269, 0.577350269, -1, 1}