x^6-85x^5+166x^4=0

Solution for x^6-85x^5+166x^4=0 equation:

Simplifying
x6 + -85x5 + 166x4 = 0

Reorder the terms:
166x4 + -85x5 + x6 = 0

Solving
166x4 + -85x5 + x6 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x4'.
x4(166 + -85x + x2) = 0

Factor a trinomial.
x4((2 + -1x)(83 + -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 '(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
Subproblem 3
Set the factor '(83 + -1x)' equal to zero and attempt to solve:

Simplifying
83 + -1x = 0

Solving
83 + -1x = 0

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

Add '-83' to each side of the equation.
83 + -83 + -1x = 0 + -83

Combine like terms: 83 + -83 = 0
0 + -1x = 0 + -83
-1x = 0 + -83

Combine like terms: 0 + -83 = -83
-1x = -83

Divide each side by '-1'.
x = 83

Simplifying
x = 83
Solution
x = {2, 83}