(x+6)x(x+9)=

Solution for (x+6)x(x+9)= equation:

Simplifying
(x + 6) * x(x + 9) = 0

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

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

Reorder the terms for easier multiplication:
x(6 + x)(9 + x) = 0

Multiply (6 + x) * (9 + x)
x(6(9 + x) + x(9 + x)) = 0
x((9 * 6 + x * 6) + x(9 + x)) = 0
x((54 + 6x) + x(9 + x)) = 0
x(54 + 6x + (9 * x + x * x)) = 0
x(54 + 6x + (9x + x2)) = 0

Combine like terms: 6x + 9x = 15x
x(54 + 15x + x2) = 0
(54 * x + 15x * x + x2 * x) = 0
(54x + 15x2 + x3) = 0

Solving
54x + 15x2 + x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(54 + 15x + x2) = 0

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

Simplifying
9 + x = 0

Solving
9 + x = 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 + x = 0 + -9

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

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

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

Simplifying
6 + x = 0

Solving
6 + x = 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 + x = 0 + -6

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

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

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