x^3-15x^2+71x=0

Solution for x^3-15x^2+71x=0 equation:

Simplifying
x3 + -15x2 + 71x = 0

Reorder the terms:
71x + -15x2 + x3 = 0

Solving
71x + -15x2 + x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(71 + -15x + 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 '(71 + -15x + x2)' equal to zero and attempt to solve:

Simplifying
71 + -15x + x2 = 0

Solving
71 + -15x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-71' to each side of the equation.
71 + -15x + -71 + x2 = 0 + -71

Reorder the terms:
71 + -71 + -15x + x2 = 0 + -71

Combine like terms: 71 + -71 = 0
0 + -15x + x2 = 0 + -71
-15x + x2 = 0 + -71

Combine like terms: 0 + -71 = -71
-15x + x2 = -71

The x term is -15x.  Take half its coefficient (-7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
-15x + 56.25 + x2 = -71 + 56.25

Reorder the terms:
56.25 + -15x + x2 = -71 + 56.25

Combine like terms: -71 + 56.25 = -14.75
56.25 + -15x + x2 = -14.75

Factor a perfect square on the left side:
(x + -7.5)(x + -7.5) = -14.75

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}