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

Factor a trinomial.
x((-6 + -1x)(9 + -1x)) = 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 '(-6 + -1x)' equal to zero and attempt to solve:

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x = 0 + 6
-1x = 0 + 6

Combine like terms: 0 + 6 = 6
-1x = 6

Divide each side by '-1'.
x = -6

Simplifying
x = -6
Subproblem 3
Set the factor '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {0, -6, 9}