2(x+3)(x+6)=0

Solution for 2(x+3)(x+6)=0 equation:

Simplifying
2(x + 3)(x + 6) = 0

Reorder the terms:
2(3 + x)(x + 6) = 0

Reorder the terms:
2(3 + x)(6 + x) = 0

Multiply (3 + x) * (6 + x)
2(3(6 + x) + x(6 + x)) = 0
2((6 * 3 + x * 3) + x(6 + x)) = 0
2((18 + 3x) + x(6 + x)) = 0
2(18 + 3x + (6 * x + x * x)) = 0
2(18 + 3x + (6x + x2)) = 0

Combine like terms: 3x + 6x = 9x
2(18 + 9x + x2) = 0
(18 * 2 + 9x * 2 + x2 * 2) = 0
(36 + 18x + 2x2) = 0

Solving
36 + 18x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(18 + 9x + x2) = 0

Factor a trinomial.
2((6 + x)(3 + x)) = 0

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
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 = {-6, -3}