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

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

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

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

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

Multiply (6 + w) * (2 + w)
2w(6(2 + w) + w(2 + w)) = 0
2w((2 * 6 + w * 6) + w(2 + w)) = 0
2w((12 + 6w) + w(2 + w)) = 0
2w(12 + 6w + (2 * w + w * w)) = 0
2w(12 + 6w + (2w + w2)) = 0

Combine like terms: 6w + 2w = 8w
2w(12 + 8w + w2) = 0
(12 * 2w + 8w * 2w + w2 * 2w) = 0
(24w + 16w2 + 2w3) = 0

Solving
24w + 16w2 + 2w3 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '2w'.
2w(12 + 8w + w2) = 0

Factor a trinomial.
2w((6 + w)(2 + 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 '(2 + w)' equal to zero and attempt to solve:

Simplifying
2 + w = 0

Solving
2 + w = 0

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

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

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

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

Simplifying
w = -2
Solution
w = {0, -6, -2}