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

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

Simplifying
4c4 + -13c2 + 3 = 0

Reorder the terms:
3 + -13c2 + 4c4 = 0

Solving
3 + -13c2 + 4c4 = 0

Solving for variable 'c'.

Factor a trinomial.
(1 + -4c2)(3 + -1c2) = 0

Factor a difference between two squares.
((1 + 2c)(1 + -2c))(3 + -1c2) = 0

Subproblem 1
Set the factor '(3 + -1c2)' equal to zero and attempt to solve:

Simplifying
3 + -1c2 = 0

Solving
3 + -1c2 = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1c2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1c2 = 0 + -3
-1c2 = 0 + -3

Combine like terms: 0 + -3 = -3
-1c2 = -3

Divide each side by '-1'.
c2 = 3

Simplifying
c2 = 3

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

Simplifying
1 + 2c = 0

Solving
1 + 2c = 0

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

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

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

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

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

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

Simplifying
1 + -2c = 0

Solving
1 + -2c = 0

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

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

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

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

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

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