5w(w-3)(w+9)=0

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Solution for 5w(w-3)(w+9)=0 equation:


Simplifying
5w(w + -3)(w + 9) = 0

Reorder the terms:
5w(-3 + w)(w + 9) = 0

Reorder the terms:
5w(-3 + w)(9 + w) = 0

Multiply (-3 + w) * (9 + w)
5w(-3(9 + w) + w(9 + w)) = 0
5w((9 * -3 + w * -3) + w(9 + w)) = 0
5w((-27 + -3w) + w(9 + w)) = 0
5w(-27 + -3w + (9 * w + w * w)) = 0
5w(-27 + -3w + (9w + w2)) = 0

Combine like terms: -3w + 9w = 6w
5w(-27 + 6w + w2) = 0
(-27 * 5w + 6w * 5w + w2 * 5w) = 0
(-135w + 30w2 + 5w3) = 0

Solving
-135w + 30w2 + 5w3 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '5w'.
5w(-27 + 6w + w2) = 0

Factor a trinomial.
5w((-9 + -1w)(3 + -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 '(-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

Subproblem 3

Set the factor '(3 + -1w)' equal to zero and attempt to solve: Simplifying 3 + -1w = 0 Solving 3 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1w = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1w = 0 + -3 -1w = 0 + -3 Combine like terms: 0 + -3 = -3 -1w = -3 Divide each side by '-1'. w = 3 Simplifying w = 3

Solution

w = {0, -9, 3}

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