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

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

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

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

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

Multiply (6 + w) * (3 + w)
2(6(3 + w) + w(3 + w)) = 0
2((3 * 6 + w * 6) + w(3 + w)) = 0
2((18 + 6w) + w(3 + w)) = 0
2(18 + 6w + (3 * w + w * w)) = 0
2(18 + 6w + (3w + w2)) = 0

Combine like terms: 6w + 3w = 9w
2(18 + 9w + w2) = 0
(18 * 2 + 9w * 2 + w2 * 2) = 0
(36 + 18w + 2w2) = 0

Solving
36 + 18w + 2w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '2'.
2(18 + 9w + w2) = 0

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

Ignore the factor 2.
Subproblem 1
Set the factor '(6 + w)' equal to zero and attempt to solve:

Simplifying
6 + w = 0

Solving
6 + w = 0

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

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

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

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

Simplifying
w = -6
Subproblem 2
Set the factor '(3 + w)' equal to zero and attempt to solve:

Simplifying
3 + w = 0

Solving
3 + w = 0

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

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

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

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

Simplifying
w = -3
Solution
w = {-6, -3}