0=3(x+2)(9+x)

Solution for 0=3(x+2)(9+x) equation:

Simplifying
0 = 3(x + 2)(9 + x)

Reorder the terms:
0 = 3(2 + x)(9 + x)

Multiply (2 + x) * (9 + x)
0 = 3(2(9 + x) + x(9 + x))
0 = 3((9 * 2 + x * 2) + x(9 + x))
0 = 3((18 + 2x) + x(9 + x))
0 = 3(18 + 2x + (9 * x + x * x))
0 = 3(18 + 2x + (9x + x2))

Combine like terms: 2x + 9x = 11x
0 = 3(18 + 11x + x2)
0 = (18 * 3 + 11x * 3 + x2 * 3)
0 = (54 + 33x + 3x2)

Solving
0 = 54 + 33x + 3x2

Solving for variable 'x'.

Combine like terms: 0 + -54 = -54
-54 + -33x + -3x2 = 54 + 33x + 3x2 + -54 + -33x + -3x2

Reorder the terms:
-54 + -33x + -3x2 = 54 + -54 + 33x + -33x + 3x2 + -3x2

Combine like terms: 54 + -54 = 0
-54 + -33x + -3x2 = 0 + 33x + -33x + 3x2 + -3x2
-54 + -33x + -3x2 = 33x + -33x + 3x2 + -3x2

Combine like terms: 33x + -33x = 0
-54 + -33x + -3x2 = 0 + 3x2 + -3x2
-54 + -33x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-54 + -33x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '-3'.
-3(18 + 11x + x2) = 0

Factor a trinomial.
-3((9 + x)(2 + x)) = 0

Ignore the factor -3.
Subproblem 1
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 2
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2
Solution
x = {-9, -2}