x^2(x+6)-9x(x-6)=0

Solution for x^2(x+6)-9x(x-6)=0 equation:

Simplifying
x2(x + 6) + -9x(x + -6) = 0

Reorder the terms:
x2(6 + x) + -9x(x + -6) = 0
(6 * x2 + x * x2) + -9x(x + -6) = 0
(6x2 + x3) + -9x(x + -6) = 0

Reorder the terms:
6x2 + x3 + -9x(-6 + x) = 0
6x2 + x3 + (-6 * -9x + x * -9x) = 0
6x2 + x3 + (54x + -9x2) = 0

Reorder the terms:
54x + 6x2 + -9x2 + x3 = 0

Combine like terms: 6x2 + -9x2 = -3x2
54x + -3x2 + x3 = 0

Solving
54x + -3x2 + x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(54 + -3x + 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 '(54 + -3x + x2)' equal to zero and attempt to solve:

Simplifying
54 + -3x + x2 = 0

Solving
54 + -3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-54' to each side of the equation.
54 + -3x + -54 + x2 = 0 + -54

Reorder the terms:
54 + -54 + -3x + x2 = 0 + -54

Combine like terms: 54 + -54 = 0
0 + -3x + x2 = 0 + -54
-3x + x2 = 0 + -54

Combine like terms: 0 + -54 = -54
-3x + x2 = -54

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = -54 + 2.25

Reorder the terms:
2.25 + -3x + x2 = -54 + 2.25

Combine like terms: -54 + 2.25 = -51.75
2.25 + -3x + x2 = -51.75

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = -51.75

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}