w(2w+12)=54

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Solution for w(2w+12)=54 equation:


Simplifying
w(2w + 12) = 54

Reorder the terms:
w(12 + 2w) = 54
(12 * w + 2w * w) = 54
(12w + 2w2) = 54

Solving
12w + 2w2 = 54

Solving for variable 'w'.

Reorder the terms:
-54 + 12w + 2w2 = 54 + -54

Combine like terms: 54 + -54 = 0
-54 + 12w + 2w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-27 + 6w + w2) = 0

Factor a trinomial.
2((-9 + -1w)(3 + -1w)) = 0

Ignore the factor 2.

Subproblem 1

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

Subproblem 2

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 = {-9, 3}

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