(x+3)x(x+9)=

Solution for (x+3)x(x+9)= equation:

Simplifying
(x + 3) * x(x + 9) = 0

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

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

Reorder the terms for easier multiplication:
x(3 + x)(9 + x) = 0

Multiply (3 + x) * (9 + x)
x(3(9 + x) + x(9 + x)) = 0
x((9 * 3 + x * 3) + x(9 + x)) = 0
x((27 + 3x) + x(9 + x)) = 0
x(27 + 3x + (9 * x + x * x)) = 0
x(27 + 3x + (9x + x2)) = 0

Combine like terms: 3x + 9x = 12x
x(27 + 12x + x2) = 0
(27 * x + 12x * x + x2 * x) = 0
(27x + 12x2 + x3) = 0

Solving
27x + 12x2 + x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(27 + 12x + x2) = 0

Factor a trinomial.
x((9 + x)(3 + 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 '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

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

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

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

Simplifying
x = -3
Solution
x = {0, -9, -3}