2k^6=18k^4

Solution for 2k^6=18k^4 equation:

Simplifying
2k6 = 18k4

Solving
2k6 = 18k4

Solving for variable 'k'.

Reorder the terms:
-18k4 + 2k6 = 18k4 + -18k4

Combine like terms: 18k4 + -18k4 = 0
-18k4 + 2k6 = 0

Factor out the Greatest Common Factor (GCF), '2k4'.
2k4(-9 + k2) = 0

Factor a difference between two squares.
2k4((3 + k)(-3 + k)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor 'k4' equal to zero and attempt to solve:

Simplifying
k4 = 0

Solving
k4 = 0

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

Simplifying
k4 = 0

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 '(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 + 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
Solution
k = {-3, 3}