2w(w+5)(w+4)=0

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Solution for 2w(w+5)(w+4)=0 equation: 


Simplifying
2w(w + 5)(w + 4) = 0

Reorder the terms:
2w(5 + w)(w + 4) = 0

Reorder the terms:
2w(5 + w)(4 + w) = 0

Multiply (5 + w) * (4 + w)
2w(5(4 + w) + w(4 + w)) = 0
2w((4 * 5 + w * 5) + w(4 + w)) = 0
2w((20 + 5w) + w(4 + w)) = 0
2w(20 + 5w + (4 * w + w * w)) = 0
2w(20 + 5w + (4w + w2)) = 0

Combine like terms: 5w + 4w = 9w
2w(20 + 9w + w2) = 0
(20 * 2w + 9w * 2w + w2 * 2w) = 0
(40w + 18w2 + 2w3) = 0

Solving
40w + 18w2 + 2w3 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '2w'.
2w(20 + 9w + w2) = 0

Factor a trinomial.
2w((5 + w)(4 + 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 '(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

Subproblem 3
Set the factor '(4 + w)' equal to zero and attempt to solve:

Simplifying
4 + w = 0

Solving
4 + w = 0

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

Add '-4' to each side of the equation.
4 + -4 + w = 0 + -4

Combine like terms: 4 + -4 = 0
0 + w = 0 + -4
w = 0 + -4

Combine like terms: 0 + -4 = -4
w = -4

Simplifying
w = -4
Solution
w = {0, -5, -4}

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