0=x^6-8x^5+12x^4

Solution for 0=x^6-8x^5+12x^4 equation:

Simplifying
0 = x6 + -8x5 + 12x4

Reorder the terms:
0 = 12x4 + -8x5 + x6

Solving
0 = 12x4 + -8x5 + x6

Solving for variable 'x'.
Remove the zero:
-12x4 + 8x5 + -1x6 = 12x4 + -8x5 + x6 + -12x4 + 8x5 + -1x6

Reorder the terms:
-12x4 + 8x5 + -1x6 = 12x4 + -12x4 + -8x5 + 8x5 + x6 + -1x6

Combine like terms: 12x4 + -12x4 = 0
-12x4 + 8x5 + -1x6 = 0 + -8x5 + 8x5 + x6 + -1x6
-12x4 + 8x5 + -1x6 = -8x5 + 8x5 + x6 + -1x6

Combine like terms: -8x5 + 8x5 = 0
-12x4 + 8x5 + -1x6 = 0 + x6 + -1x6
-12x4 + 8x5 + -1x6 = x6 + -1x6

Combine like terms: x6 + -1x6 = 0
-12x4 + 8x5 + -1x6 = 0

Factor out the Greatest Common Factor (GCF), 'x4'.
x4(-12 + 8x + -1x2) = 0

Factor a trinomial.
x4((-6 + x)(2 + -1x)) = 0

Subproblem 1
Set the factor 'x4' equal to zero and attempt to solve:

Simplifying
x4 = 0

Solving
x4 = 0

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

Simplifying
x4 = 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 + x)' equal to zero and attempt to solve:

Simplifying
-6 + x = 0

Solving
-6 + x = 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 + x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + x = 0 + 6
x = 0 + 6

Combine like terms: 0 + 6 = 6
x = 6

Simplifying
x = 6
Subproblem 3
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {6, 2}