c^4-9c^2+20=0

Solution for c^4-9c^2+20=0 equation:

Simplifying
c4 + -9c2 + 20 = 0

Reorder the terms:
20 + -9c2 + c4 = 0

Solving
20 + -9c2 + c4 = 0

Solving for variable 'c'.

Factor a trinomial.
(4 + -1c2)(5 + -1c2) = 0

Factor a difference between two squares.
((2 + c)(2 + -1c))(5 + -1c2) = 0

Subproblem 1
Set the factor '(5 + -1c2)' equal to zero and attempt to solve:

Simplifying
5 + -1c2 = 0

Solving
5 + -1c2 = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1c2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1c2 = 0 + -5
-1c2 = 0 + -5

Combine like terms: 0 + -5 = -5
-1c2 = -5

Divide each side by '-1'.
c2 = 5

Simplifying
c2 = 5

Take the square root of each side:
c = {-2.236067978, 2.236067978}
Subproblem 2
Set the factor '(2 + c)' equal to zero and attempt to solve:

Simplifying
2 + c = 0

Solving
2 + c = 0

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

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

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

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

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

Simplifying
2 + -1c = 0

Solving
2 + -1c = 0

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

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

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

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

Divide each side by '-1'.
c = 2

Simplifying
c = 2
Solution
c = {-2.236067978, 2.236067978, -2, 2}