4k^4-13k^2+3=0

Solution for 4k^4-13k^2+3=0 equation:

Simplifying
4k4 + -13k2 + 3 = 0

Reorder the terms:
3 + -13k2 + 4k4 = 0

Solving
3 + -13k2 + 4k4 = 0

Solving for variable 'k'.

Factor a trinomial.
(1 + -4k2)(3 + -1k2) = 0

Factor a difference between two squares.
((1 + 2k)(1 + -2k))(3 + -1k2) = 0

Subproblem 1
Set the factor '(3 + -1k2)' equal to zero and attempt to solve:

Simplifying
3 + -1k2 = 0

Solving
3 + -1k2 = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1k2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1k2 = 0 + -3
-1k2 = 0 + -3

Combine like terms: 0 + -3 = -3
-1k2 = -3

Divide each side by '-1'.
k2 = 3

Simplifying
k2 = 3

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

Simplifying
1 + 2k = 0

Solving
1 + 2k = 0

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

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

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

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

Divide each side by '2'.
k = -0.5

Simplifying
k = -0.5
Subproblem 3
Set the factor '(1 + -2k)' equal to zero and attempt to solve:

Simplifying
1 + -2k = 0

Solving
1 + -2k = 0

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

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

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

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

Divide each side by '-2'.
k = 0.5

Simplifying
k = 0.5
Solution
k = {-1.732050808, 1.732050808, -0.5, 0.5}