2y^2+7y=-3

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


Simplifying
2y2 + 7y = -3

Reorder the terms:
7y + 2y2 = -3

Solving
7y + 2y2 = -3

Solving for variable 'y'.

Reorder the terms:
3 + 7y + 2y2 = -3 + 3

Combine like terms: -3 + 3 = 0
3 + 7y + 2y2 = 0

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

Subproblem 1

Set the factor '(3 + y)' equal to zero and attempt to solve: Simplifying 3 + y = 0 Solving 3 + y = 0 Move all terms containing y to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + y = 0 + -3 Combine like terms: 3 + -3 = 0 0 + y = 0 + -3 y = 0 + -3 Combine like terms: 0 + -3 = -3 y = -3 Simplifying y = -3

Subproblem 2

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

Solution

y = {-3, -0.5}

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