(6+w)*w=72

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Solution for (6+w)*w=72 equation:


Simplifying
(6 + w) * w = 72

Reorder the terms for easier multiplication:
w(6 + w) = 72
(6 * w + w * w) = 72
(6w + w2) = 72

Solving
6w + w2 = 72

Solving for variable 'w'.

Reorder the terms:
-72 + 6w + w2 = 72 + -72

Combine like terms: 72 + -72 = 0
-72 + 6w + w2 = 0

Factor a trinomial.
(-12 + -1w)(6 + -1w) = 0

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 '(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 = {-12, 6}

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