-12z^6=-6z^4

Solution for -12z^6=-6z^4 equation:

Simplifying
-12z6 = -6z4

Solving
-12z6 = -6z4

Solving for variable 'z'.

Reorder the terms:
6z4 + -12z6 = -6z4 + 6z4

Combine like terms: -6z4 + 6z4 = 0
6z4 + -12z6 = 0

Factor out the Greatest Common Factor (GCF), '6z4'.
6z4(1 + -2z2) = 0

Ignore the factor 6.
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 + -2z2)' equal to zero and attempt to solve:

Simplifying
1 + -2z2 = 0

Solving
1 + -2z2 = 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 + -2z2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2z2 = 0 + -1
-2z2 = 0 + -1

Combine like terms: 0 + -1 = -1
-2z2 = -1

Divide each side by '-2'.
z2 = 0.5

Simplifying
z2 = 0.5

Take the square root of each side:
z = {-0.707106781, 0.707106781}
Solution
z = {-0.707106781, 0.707106781}