2j^6-2j^2=0

Solution for 2j^6-2j^2=0 equation:

Simplifying
2j6 + -2j2 = 0

Reorder the terms:
-2j2 + 2j6 = 0

Solving
-2j2 + 2j6 = 0

Solving for variable 'j'.

Factor out the Greatest Common Factor (GCF), '2j2'.
2j2(-1 + j4) = 0

Factor a difference between two squares.
2j2((1 + j2)(-1 + j2)) = 0

Factor a difference between two squares.
2j2((1 + j2)((1 + j)(-1 + j))) = 0

Ignore the factor 2.
Subproblem 1
Set the factor 'j2' equal to zero and attempt to solve:

Simplifying
j2 = 0

Solving
j2 = 0

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

Simplifying
j2 = 0

Take the square root of each side:
j = {0}
Subproblem 2
Set the factor '(1 + j2)' equal to zero and attempt to solve:

Simplifying
1 + j2 = 0

Solving
1 + j2 = 0

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

Add '-1' to each side of the equation.
1 + -1 + j2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + j2 = 0 + -1
j2 = 0 + -1

Combine like terms: 0 + -1 = -1
j2 = -1

Simplifying
j2 = -1

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 3
Set the factor '(1 + j)' equal to zero and attempt to solve:

Simplifying
1 + j = 0

Solving
1 + j = 0

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

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

Combine like terms: 1 + -1 = 0
0 + j = 0 + -1
j = 0 + -1

Combine like terms: 0 + -1 = -1
j = -1

Simplifying
j = -1
Subproblem 4
Set the factor '(-1 + j)' equal to zero and attempt to solve:

Simplifying
-1 + j = 0

Solving
-1 + j = 0

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

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

Combine like terms: -1 + 1 = 0
0 + j = 0 + 1
j = 0 + 1

Combine like terms: 0 + 1 = 1
j = 1

Simplifying
j = 1
Solution
j = {0, -1, 1}