w(w-3)(w+15)=0

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Solution for w(w-3)(w+15)=0 equation:


Simplifying
w(w + -3)(w + 15) = 0

Reorder the terms:
w(-3 + w)(w + 15) = 0

Reorder the terms:
w(-3 + w)(15 + w) = 0

Multiply (-3 + w) * (15 + w)
w(-3(15 + w) + w(15 + w)) = 0
w((15 * -3 + w * -3) + w(15 + w)) = 0
w((-45 + -3w) + w(15 + w)) = 0
w(-45 + -3w + (15 * w + w * w)) = 0
w(-45 + -3w + (15w + w2)) = 0

Combine like terms: -3w + 15w = 12w
w(-45 + 12w + w2) = 0
(-45 * w + 12w * w + w2 * w) = 0
(-45w + 12w2 + w3) = 0

Solving
-45w + 12w2 + w3 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), 'w'.
w(-45 + 12w + w2) = 0

Factor a trinomial.
w((-15 + -1w)(3 + -1w)) = 0

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 '(-15 + -1w)' equal to zero and attempt to solve: Simplifying -15 + -1w = 0 Solving -15 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + -1w = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -1w = 0 + 15 -1w = 0 + 15 Combine like terms: 0 + 15 = 15 -1w = 15 Divide each side by '-1'. w = -15 Simplifying w = -15

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, -15, 3}

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