2k^4-3k^2=20

Solution for 2k^4-3k^2=20 equation:

Simplifying
2k4 + -3k2 = 20

Reorder the terms:
-3k2 + 2k4 = 20

Solving
-3k2 + 2k4 = 20

Solving for variable 'k'.

Reorder the terms:
-20 + -3k2 + 2k4 = 20 + -20

Combine like terms: 20 + -20 = 0
-20 + -3k2 + 2k4 = 0

Factor a trinomial.
(-5 + -2k2)(4 + -1k2) = 0

Factor a difference between two squares.
(-5 + -2k2)((2 + k)(2 + -1k)) = 0

Subproblem 1
Set the factor '(-5 + -2k2)' equal to zero and attempt to solve:

Simplifying
-5 + -2k2 = 0

Solving
-5 + -2k2 = 0

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

Add '5' to each side of the equation.
-5 + 5 + -2k2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2k2 = 0 + 5
-2k2 = 0 + 5

Combine like terms: 0 + 5 = 5
-2k2 = 5

Divide each side by '-2'.
k2 = -2.5

Simplifying
k2 = -2.5

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(2 + k)' equal to zero and attempt to solve:

Simplifying
2 + k = 0

Solving
2 + k = 0

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

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

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

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

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

Simplifying
2 + -1k = 0

Solving
2 + -1k = 0

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

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

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

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

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

Simplifying
k = 2
Solution
k = {-2, 2}