2w(w+7)(w-1)=0

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Solution for 2w(w+7)(w-1)=0 equation:


Simplifying
2w(w + 7)(w + -1) = 0

Reorder the terms:
2w(7 + w)(w + -1) = 0

Reorder the terms:
2w(7 + w)(-1 + w) = 0

Multiply (7 + w) * (-1 + w)
2w(7(-1 + w) + w(-1 + w)) = 0
2w((-1 * 7 + w * 7) + w(-1 + w)) = 0
2w((-7 + 7w) + w(-1 + w)) = 0
2w(-7 + 7w + (-1 * w + w * w)) = 0
2w(-7 + 7w + (-1w + w2)) = 0

Combine like terms: 7w + -1w = 6w
2w(-7 + 6w + w2) = 0
(-7 * 2w + 6w * 2w + w2 * 2w) = 0
(-14w + 12w2 + 2w3) = 0

Solving
-14w + 12w2 + 2w3 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '2w'.
2w(-7 + 6w + w2) = 0

Factor a trinomial.
2w((-7 + -1w)(1 + -1w)) = 0

Ignore the factor 2.

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

Solution

w = {0, -7, 1}

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