5w(w-8)(w+7)=0

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Solution for 5w(w-8)(w+7)=0 equation:


Simplifying
5w(w + -8)(w + 7) = 0

Reorder the terms:
5w(-8 + w)(w + 7) = 0

Reorder the terms:
5w(-8 + w)(7 + w) = 0

Multiply (-8 + w) * (7 + w)
5w(-8(7 + w) + w(7 + w)) = 0
5w((7 * -8 + w * -8) + w(7 + w)) = 0
5w((-56 + -8w) + w(7 + w)) = 0
5w(-56 + -8w + (7 * w + w * w)) = 0
5w(-56 + -8w + (7w + w2)) = 0

Combine like terms: -8w + 7w = -1w
5w(-56 + -1w + w2) = 0
(-56 * 5w + -1w * 5w + w2 * 5w) = 0
(-280w + -5w2 + 5w3) = 0

Solving
-280w + -5w2 + 5w3 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '5w'.
5w(-56 + -1w + w2) = 0

Factor a trinomial.
5w((-7 + -1w)(8 + -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 '(-7 + -1w)' equal to zero and attempt to solve: Simplifying -7 + -1w = 0 Solving -7 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -1w = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1w = 0 + 7 -1w = 0 + 7 Combine like terms: 0 + 7 = 7 -1w = 7 Divide each side by '-1'. w = -7 Simplifying w = -7

Subproblem 3

Set the factor '(8 + -1w)' equal to zero and attempt to solve: Simplifying 8 + -1w = 0 Solving 8 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1w = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1w = 0 + -8 -1w = 0 + -8 Combine like terms: 0 + -8 = -8 -1w = -8 Divide each side by '-1'. w = 8 Simplifying w = 8

Solution

w = {0, -7, 8}

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