0=12x^8-72x^6

Solution for 0=12x^8-72x^6 equation:

Simplifying
0 = 12x8 + -72x6

Reorder the terms:
0 = -72x6 + 12x8

Solving
0 = -72x6 + 12x8

Solving for variable 'x'.
Remove the zero:
72x6 + -12x8 = -72x6 + 12x8 + 72x6 + -12x8

Reorder the terms:
72x6 + -12x8 = -72x6 + 72x6 + 12x8 + -12x8

Combine like terms: -72x6 + 72x6 = 0
72x6 + -12x8 = 0 + 12x8 + -12x8
72x6 + -12x8 = 12x8 + -12x8

Combine like terms: 12x8 + -12x8 = 0
72x6 + -12x8 = 0

Factor out the Greatest Common Factor (GCF), '12x6'.
12x6(6 + -1x2) = 0

Ignore the factor 12.
Subproblem 1
Set the factor 'x6' equal to zero and attempt to solve:

Simplifying
x6 = 0

Solving
x6 = 0

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

Simplifying
x6 = 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 '(6 + -1x2)' equal to zero and attempt to solve:

Simplifying
6 + -1x2 = 0

Solving
6 + -1x2 = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x2 = 0 + -6
-1x2 = 0 + -6

Combine like terms: 0 + -6 = -6
-1x2 = -6

Divide each side by '-1'.
x2 = 6

Simplifying
x2 = 6

Take the square root of each side:
x = {-2.449489743, 2.449489743}
Solution
x = {-2.449489743, 2.449489743}