-12y=4y^2+9

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Solution for -12y=4y^2+9 equation:


Simplifying
-12y = 4y2 + 9

Reorder the terms:
-12y = 9 + 4y2

Solving
-12y = 9 + 4y2

Solving for variable 'y'.

Reorder the terms:
-9 + -12y + -4y2 = 9 + 4y2 + -9 + -4y2

Reorder the terms:
-9 + -12y + -4y2 = 9 + -9 + 4y2 + -4y2

Combine like terms: 9 + -9 = 0
-9 + -12y + -4y2 = 0 + 4y2 + -4y2
-9 + -12y + -4y2 = 4y2 + -4y2

Combine like terms: 4y2 + -4y2 = 0
-9 + -12y + -4y2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(9 + 12y + 4y2) = 0

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

Ignore the factor -1.

Subproblem 1

Set the factor '(3 + 2y)' equal to zero and attempt to solve: Simplifying 3 + 2y = 0 Solving 3 + 2y = 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 + 2y = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2y = 0 + -3 2y = 0 + -3 Combine like terms: 0 + -3 = -3 2y = -3 Divide each side by '2'. y = -1.5 Simplifying y = -1.5

Subproblem 2

Set the factor '(3 + 2y)' equal to zero and attempt to solve: Simplifying 3 + 2y = 0 Solving 3 + 2y = 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 + 2y = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2y = 0 + -3 2y = 0 + -3 Combine like terms: 0 + -3 = -3 2y = -3 Divide each side by '2'. y = -1.5 Simplifying y = -1.5

Solution

y = {-1.5, -1.5}

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