-2k^4=-18k^2

Solution for -2k^4=-18k^2 equation:

Simplifying
-2k4 = -18k2

Solving
-2k4 = -18k2

Solving for variable 'k'.

Reorder the terms:
18k2 + -2k4 = -18k2 + 18k2

Combine like terms: -18k2 + 18k2 = 0
18k2 + -2k4 = 0

Factor out the Greatest Common Factor (GCF), '2k2'.
2k2(9 + -1k2) = 0

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

Ignore the factor 2.
Subproblem 1
Set the factor 'k2' equal to zero and attempt to solve:

Simplifying
k2 = 0

Solving
k2 = 0

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

Simplifying
k2 = 0

Take the square root of each side:
k = {0}
Subproblem 2
Set the factor '(3 + k)' equal to zero and attempt to solve:

Simplifying
3 + k = 0

Solving
3 + k = 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 + k = 0 + -3

Combine like terms: 3 + -3 = 0
0 + k = 0 + -3
k = 0 + -3

Combine like terms: 0 + -3 = -3
k = -3

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

Simplifying
3 + -1k = 0

Solving
3 + -1k = 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 + -1k = 0 + -3

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

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

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

Simplifying
k = 3
Solution
k = {0, -3, 3}