2y^2+4=-9y

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Solution for 2y^2+4=-9y equation:


Simplifying
2y2 + 4 = -9y

Reorder the terms:
4 + 2y2 = -9y

Solving
4 + 2y2 = -9y

Solving for variable 'y'.

Reorder the terms:
4 + 9y + 2y2 = -9y + 9y

Combine like terms: -9y + 9y = 0
4 + 9y + 2y2 = 0

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

Subproblem 1

Set the factor '(4 + y)' equal to zero and attempt to solve: Simplifying 4 + y = 0 Solving 4 + y = 0 Move all terms containing y to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + y = 0 + -4 Combine like terms: 4 + -4 = 0 0 + y = 0 + -4 y = 0 + -4 Combine like terms: 0 + -4 = -4 y = -4 Simplifying y = -4

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 = {-4, -0.5}

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