180=3w+w^2

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Solution for 180=3w+w^2 equation:


Simplifying
180 = 3w + w2

Solving
180 = 3w + w2

Solving for variable 'w'.

Reorder the terms:
180 + -3w + -1w2 = 3w + -3w + w2 + -1w2

Combine like terms: 3w + -3w = 0
180 + -3w + -1w2 = 0 + w2 + -1w2
180 + -3w + -1w2 = w2 + -1w2

Combine like terms: w2 + -1w2 = 0
180 + -3w + -1w2 = 0

Factor a trinomial.
(12 + -1w)(15 + w) = 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 '(15 + w)' equal to zero and attempt to solve: Simplifying 15 + w = 0 Solving 15 + w = 0 Move all terms containing w to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + w = 0 + -15 Combine like terms: 15 + -15 = 0 0 + w = 0 + -15 w = 0 + -15 Combine like terms: 0 + -15 = -15 w = -15 Simplifying w = -15

Solution

w = {12, -15}

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