x^3-13x^2+80x=0

Solution for x^3-13x^2+80x=0 equation:

Simplifying
x3 + -13x2 + 80x = 0

Reorder the terms:
80x + -13x2 + x3 = 0

Solving
80x + -13x2 + x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(80 + -13x + 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 '(80 + -13x + x2)' equal to zero and attempt to solve:

Simplifying
80 + -13x + x2 = 0

Solving
80 + -13x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-80' to each side of the equation.
80 + -13x + -80 + x2 = 0 + -80

Reorder the terms:
80 + -80 + -13x + x2 = 0 + -80

Combine like terms: 80 + -80 = 0
0 + -13x + x2 = 0 + -80
-13x + x2 = 0 + -80

Combine like terms: 0 + -80 = -80
-13x + x2 = -80

The x term is -13x.  Take half its coefficient (-6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
-13x + 42.25 + x2 = -80 + 42.25

Reorder the terms:
42.25 + -13x + x2 = -80 + 42.25

Combine like terms: -80 + 42.25 = -37.75
42.25 + -13x + x2 = -37.75

Factor a perfect square on the left side:
(x + -6.5)(x + -6.5) = -37.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}