4y^2+12y=-5

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Solution for 4y^2+12y=-5 equation:


Simplifying
4y2 + 12y = -5

Reorder the terms:
12y + 4y2 = -5

Solving
12y + 4y2 = -5

Solving for variable 'y'.

Reorder the terms:
5 + 12y + 4y2 = -5 + 5

Combine like terms: -5 + 5 = 0
5 + 12y + 4y2 = 0

Factor a trinomial.
(5 + 2y)(1 + 2y) = 0

Subproblem 1

Set the factor '(5 + 2y)' equal to zero and attempt to solve: Simplifying 5 + 2y = 0 Solving 5 + 2y = 0 Move all terms containing y to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 2y = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2y = 0 + -5 2y = 0 + -5 Combine like terms: 0 + -5 = -5 2y = -5 Divide each side by '2'. y = -2.5 Simplifying y = -2.5

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 = {-2.5, -0.5}

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