4c^4-37c^2+63=0

Solution for 4c^4-37c^2+63=0 equation:

Simplifying
4c4 + -37c2 + 63 = 0

Reorder the terms:
63 + -37c2 + 4c4 = 0

Solving
63 + -37c2 + 4c4 = 0

Solving for variable 'c'.

Factor a trinomial.
(9 + -4c2)(7 + -1c2) = 0

Factor a difference between two squares.
((3 + 2c)(3 + -2c))(7 + -1c2) = 0

Subproblem 1
Set the factor '(7 + -1c2)' equal to zero and attempt to solve:

Simplifying
7 + -1c2 = 0

Solving
7 + -1c2 = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1c2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1c2 = 0 + -7
-1c2 = 0 + -7

Combine like terms: 0 + -7 = -7
-1c2 = -7

Divide each side by '-1'.
c2 = 7

Simplifying
c2 = 7

Take the square root of each side:
c = {-2.645751311, 2.645751311}
Subproblem 2
Set the factor '(3 + 2c)' equal to zero and attempt to solve:

Simplifying
3 + 2c = 0

Solving
3 + 2c = 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 + 2c = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2c = 0 + -3
2c = 0 + -3

Combine like terms: 0 + -3 = -3
2c = -3

Divide each side by '2'.
c = -1.5

Simplifying
c = -1.5
Subproblem 3
Set the factor '(3 + -2c)' equal to zero and attempt to solve:

Simplifying
3 + -2c = 0

Solving
3 + -2c = 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 + -2c = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2c = 0 + -3
-2c = 0 + -3

Combine like terms: 0 + -3 = -3
-2c = -3

Divide each side by '-2'.
c = 1.5

Simplifying
c = 1.5
Solution
c = {-2.645751311, 2.645751311, -1.5, 1.5}