6y^2+12y+13-2y^2-4=0

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Solution for 6y^2+12y+13-2y^2-4=0 equation:


Simplifying
6y2 + 12y + 13 + -2y2 + -4 = 0

Reorder the terms:
13 + -4 + 12y + 6y2 + -2y2 = 0

Combine like terms: 13 + -4 = 9
9 + 12y + 6y2 + -2y2 = 0

Combine like terms: 6y2 + -2y2 = 4y2
9 + 12y + 4y2 = 0

Solving
9 + 12y + 4y2 = 0

Solving for variable 'y'.

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

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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