5w(w-9)(w+4)=0

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Solution for 5w(w-9)(w+4)=0 equation: 


Simplifying
5w(w + -9)(w + 4) = 0

Reorder the terms:
5w(-9 + w)(w + 4) = 0

Reorder the terms:
5w(-9 + w)(4 + w) = 0

Multiply (-9 + w) * (4 + w)
5w(-9(4 + w) + w(4 + w)) = 0
5w((4 * -9 + w * -9) + w(4 + w)) = 0
5w((-36 + -9w) + w(4 + w)) = 0
5w(-36 + -9w + (4 * w + w * w)) = 0
5w(-36 + -9w + (4w + w2)) = 0

Combine like terms: -9w + 4w = -5w
5w(-36 + -5w + w2) = 0
(-36 * 5w + -5w * 5w + w2 * 5w) = 0
(-180w + -25w2 + 5w3) = 0

Solving
-180w + -25w2 + 5w3 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '5w'.
5w(-36 + -5w + w2) = 0

Factor a trinomial.
5w((-4 + -1w)(9 + -1w)) = 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 '(-4 + -1w)' equal to zero and attempt to solve:

Simplifying
-4 + -1w = 0

Solving
-4 + -1w = 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 + -1w = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1w = 0 + 4
-1w = 0 + 4

Combine like terms: 0 + 4 = 4
-1w = 4

Divide each side by '-1'.
w = -4

Simplifying
w = -4

Subproblem 3
Set the factor '(9 + -1w)' equal to zero and attempt to solve:

Simplifying
9 + -1w = 0

Solving
9 + -1w = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1w = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1w = 0 + -9
-1w = 0 + -9

Combine like terms: 0 + -9 = -9
-1w = -9

Divide each side by '-1'.
w = 9

Simplifying
w = 9
Solution
w = {0, -4, 9}

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