4w(w+6)(w+5)=0

Solution for 4w(w+6)(w+5)=0 equation:

Simplifying
4w(w + 6)(w + 5) = 0

Reorder the terms:
4w(6 + w)(w + 5) = 0

Reorder the terms:
4w(6 + w)(5 + w) = 0

Multiply (6 + w) * (5 + w)
4w(6(5 + w) + w(5 + w)) = 0
4w((5 * 6 + w * 6) + w(5 + w)) = 0
4w((30 + 6w) + w(5 + w)) = 0
4w(30 + 6w + (5 * w + w * w)) = 0
4w(30 + 6w + (5w + w2)) = 0

Combine like terms: 6w + 5w = 11w
4w(30 + 11w + w2) = 0
(30 * 4w + 11w * 4w + w2 * 4w) = 0
(120w + 44w2 + 4w3) = 0

Solving
120w + 44w2 + 4w3 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '4w'.
4w(30 + 11w + w2) = 0

Factor a trinomial.
4w((6 + w)(5 + w)) = 0

Ignore the factor 4.
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 '(5 + w)' equal to zero and attempt to solve:

Simplifying
5 + w = 0

Solving
5 + w = 0

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

Add '-5' to each side of the equation.
5 + -5 + w = 0 + -5

Combine like terms: 5 + -5 = 0
0 + w = 0 + -5
w = 0 + -5

Combine like terms: 0 + -5 = -5
w = -5

Simplifying
w = -5
Solution
w = {0, -6, -5}