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

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


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

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

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

Multiply (-2 + w) * (4 + w)
-5w(-2(4 + w) + w(4 + w)) = 0
-5w((4 * -2 + w * -2) + w(4 + w)) = 0
-5w((-8 + -2w) + w(4 + w)) = 0
-5w(-8 + -2w + (4 * w + w * w)) = 0
-5w(-8 + -2w + (4w + w2)) = 0

Combine like terms: -2w + 4w = 2w
-5w(-8 + 2w + w2) = 0
(-8 * -5w + 2w * -5w + w2 * -5w) = 0
(40w + -10w2 + -5w3) = 0

Solving
40w + -10w2 + -5w3 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '5w'.
5w(8 + -2w + -1w2) = 0

Factor a trinomial.
5w((2 + -1w)(4 + w)) = 0

Ignore the factor 5.

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 '(2 + -1w)' equal to zero and attempt to solve:

Simplifying
2 + -1w = 0

Solving
2 + -1w = 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 + -1w = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1w = 0 + -2
-1w = 0 + -2

Combine like terms: 0 + -2 = -2
-1w = -2

Divide each side by '-1'.
w = 2

Simplifying
w = 2

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, 2, -4}

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