2w^2+11w-13-w^2-3w+28=0

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Solution for 2w^2+11w-13-w^2-3w+28=0 equation:


Simplifying
2w2 + 11w + -13 + -1w2 + -3w + 28 = 0

Reorder the terms:
-13 + 28 + 11w + -3w + 2w2 + -1w2 = 0

Combine like terms: -13 + 28 = 15
15 + 11w + -3w + 2w2 + -1w2 = 0

Combine like terms: 11w + -3w = 8w
15 + 8w + 2w2 + -1w2 = 0

Combine like terms: 2w2 + -1w2 = 1w2
15 + 8w + 1w2 = 0

Solving
15 + 8w + 1w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(5 + w)(3 + w) = 0

Subproblem 1

Set the factor '(5 + w)' equal to zero and attempt to solve: Simplifying 5 + w = 0 Solving 5 + w = 0 Move all terms containing w to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + w = 0 + -5 Combine like terms: 5 + -5 = 0 0 + w = 0 + -5 w = 0 + -5 Combine like terms: 0 + -5 = -5 w = -5 Simplifying w = -5

Subproblem 2

Set the factor '(3 + w)' equal to zero and attempt to solve: Simplifying 3 + w = 0 Solving 3 + w = 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 + w = 0 + -3 Combine like terms: 3 + -3 = 0 0 + w = 0 + -3 w = 0 + -3 Combine like terms: 0 + -3 = -3 w = -3 Simplifying w = -3

Solution

w = {-5, -3}

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