(-6z^4-6z^2)(6z^4-6z^2)=0

Solution for (-6z^4-6z^2)(6z^4-6z^2)=0 equation:

Simplifying
(-6z4 + -6z2)(6z4 + -6z2) = 0

Reorder the terms:
(-6z2 + -6z4)(6z4 + -6z2) = 0

Reorder the terms:
(-6z2 + -6z4)(-6z2 + 6z4) = 0

Multiply (-6z2 + -6z4) * (-6z2 + 6z4)
(-6z2 * (-6z2 + 6z4) + -6z4 * (-6z2 + 6z4)) = 0
((-6z2 * -6z2 + 6z4 * -6z2) + -6z4 * (-6z2 + 6z4)) = 0
((36z4 + -36z6) + -6z4 * (-6z2 + 6z4)) = 0
(36z4 + -36z6 + (-6z2 * -6z4 + 6z4 * -6z4)) = 0
(36z4 + -36z6 + (36z6 + -36z8)) = 0

Combine like terms: -36z6 + 36z6 = 0
(36z4 + 0 + -36z8) = 0
(36z4 + -36z8) = 0

Solving
36z4 + -36z8 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '36z4'.
36z4(1 + -1z4) = 0

Factor a difference between two squares.
36z4((1 + z2)(1 + -1z2)) = 0

Factor a difference between two squares.
36z4((1 + z2)((1 + z)(1 + -1z))) = 0

Ignore the factor 36.
Subproblem 1
Set the factor 'z4' equal to zero and attempt to solve:

Simplifying
z4 = 0

Solving
z4 = 0

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

Simplifying
z4 = 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 '(1 + z2)' equal to zero and attempt to solve:

Simplifying
1 + z2 = 0

Solving
1 + z2 = 0

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

Add '-1' to each side of the equation.
1 + -1 + z2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + z2 = 0 + -1
z2 = 0 + -1

Combine like terms: 0 + -1 = -1
z2 = -1

Simplifying
z2 = -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 + z)' equal to zero and attempt to solve:

Simplifying
1 + z = 0

Solving
1 + z = 0

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

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

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

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

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

Simplifying
1 + -1z = 0

Solving
1 + -1z = 0

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

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

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

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

Divide each side by '-1'.
z = 1

Simplifying
z = 1
Solution
z = {-1, 1}