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

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

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

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

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

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

Combine like terms: 3w + 6w = 9w
-2w(18 + 9w + w2) = 0
(18 * -2w + 9w * -2w + w2 * -2w) = 0
(-36w + -18w2 + -2w3) = 0

Solving
-36w + -18w2 + -2w3 = 0

Solving for variable 'w'.

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

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

Ignore the factor -2.
Subproblem 1
Set the factor 'w' equal to zero and attempt to solve:

Simplifying
w = 0

Solving
w = 0

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

Simplifying
w = 0
Subproblem 2
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 3
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 = {0, -6, -3}