2w^2+7w=-3

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Solution for 2w^2+7w=-3 equation:


Simplifying
2w2 + 7w = -3

Reorder the terms:
7w + 2w2 = -3

Solving
7w + 2w2 = -3

Solving for variable 'w'.

Reorder the terms:
3 + 7w + 2w2 = -3 + 3

Combine like terms: -3 + 3 = 0
3 + 7w + 2w2 = 0

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

Subproblem 1

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

Subproblem 2

Set the factor '(1 + 2w)' equal to zero and attempt to solve: Simplifying 1 + 2w = 0 Solving 1 + 2w = 0 Move all terms containing w to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2w = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2w = 0 + -1 2w = 0 + -1 Combine like terms: 0 + -1 = -1 2w = -1 Divide each side by '2'. w = -0.5 Simplifying w = -0.5

Solution

w = {-3, -0.5}

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