x^3-85x^2+4x=0

Solution for x^3-85x^2+4x=0 equation:

Simplifying
x3 + -85x2 + 4x = 0

Reorder the terms:
4x + -85x2 + x3 = 0

Solving
4x + -85x2 + x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(4 + -85x + x2) = 0

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

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(4 + -85x + x2)' equal to zero and attempt to solve:

Simplifying
4 + -85x + x2 = 0

Solving
4 + -85x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + -85x + -4 + x2 = 0 + -4

Reorder the terms:
4 + -4 + -85x + x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -85x + x2 = 0 + -4
-85x + x2 = 0 + -4

Combine like terms: 0 + -4 = -4
-85x + x2 = -4

The x term is -85x.  Take half its coefficient (-42.5).
Square it (1806.25) and add it to both sides.

Add '1806.25' to each side of the equation.
-85x + 1806.25 + x2 = -4 + 1806.25

Reorder the terms:
1806.25 + -85x + x2 = -4 + 1806.25

Combine like terms: -4 + 1806.25 = 1802.25
1806.25 + -85x + x2 = 1802.25

Factor a perfect square on the left side:
(x + -42.5)(x + -42.5) = 1802.25

Calculate the square root of the right side: 42.452915094

Break this problem into two subproblems by setting 
(x + -42.5) equal to 42.452915094 and -42.452915094.

Subproblem 1
x + -42.5 = 42.452915094

Simplifying
x + -42.5 = 42.452915094

Reorder the terms:
-42.5 + x = 42.452915094

Solving
-42.5 + x = 42.452915094

Solving for variable 'x'.

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

Add '42.5' to each side of the equation.
-42.5 + 42.5 + x = 42.452915094 + 42.5

Combine like terms: -42.5 + 42.5 = 0.0
0.0 + x = 42.452915094 + 42.5
x = 42.452915094 + 42.5

Combine like terms: 42.452915094 + 42.5 = 84.952915094
x = 84.952915094

Simplifying
x = 84.952915094

Subproblem 2
x + -42.5 = -42.452915094

Simplifying
x + -42.5 = -42.452915094

Reorder the terms:
-42.5 + x = -42.452915094

Solving
-42.5 + x = -42.452915094

Solving for variable 'x'.

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

Add '42.5' to each side of the equation.
-42.5 + 42.5 + x = -42.452915094 + 42.5

Combine like terms: -42.5 + 42.5 = 0.0
0.0 + x = -42.452915094 + 42.5
x = -42.452915094 + 42.5

Combine like terms: -42.452915094 + 42.5 = 0.047084906
x = 0.047084906

Simplifying
x = 0.047084906

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {84.952915094, 0.047084906}
Solution
x = {0, 84.952915094, 0.047084906}