w(2w+4)=96

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Solution for w(2w+4)=96 equation:


Simplifying
w(2w + 4) = 96

Reorder the terms:
w(4 + 2w) = 96
(4 * w + 2w * w) = 96
(4w + 2w2) = 96

Solving
4w + 2w2 = 96

Solving for variable 'w'.

Reorder the terms:
-96 + 4w + 2w2 = 96 + -96

Combine like terms: 96 + -96 = 0
-96 + 4w + 2w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-48 + 2w + w2) = 0

Factor a trinomial.
2((-8 + -1w)(6 + -1w)) = 0

Ignore the factor 2.

Subproblem 1

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

Subproblem 2

Set the factor '(6 + -1w)' equal to zero and attempt to solve: Simplifying 6 + -1w = 0 Solving 6 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1w = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1w = 0 + -6 -1w = 0 + -6 Combine like terms: 0 + -6 = -6 -1w = -6 Divide each side by '-1'. w = 6 Simplifying w = 6

Solution

w = {-8, 6}

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