(2w+6)w=216

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Solution for (2w+6)w=216 equation:


Simplifying
(2w + 6) * w = 216

Reorder the terms:
(6 + 2w) * w = 216

Reorder the terms for easier multiplication:
w(6 + 2w) = 216
(6 * w + 2w * w) = 216
(6w + 2w2) = 216

Solving
6w + 2w2 = 216

Solving for variable 'w'.

Reorder the terms:
-216 + 6w + 2w2 = 216 + -216

Combine like terms: 216 + -216 = 0
-216 + 6w + 2w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-108 + 3w + w2) = 0

Factor a trinomial.
2((-12 + -1w)(9 + -1w)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-12 + -1w)' equal to zero and attempt to solve: Simplifying -12 + -1w = 0 Solving -12 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + -1w = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -1w = 0 + 12 -1w = 0 + 12 Combine like terms: 0 + 12 = 12 -1w = 12 Divide each side by '-1'. w = -12 Simplifying w = -12

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

Solution

w = {-12, 9}

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