6y+2=2y^2-6

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Solution for 6y+2=2y^2-6 equation:


Simplifying
6y + 2 = 2y2 + -6

Reorder the terms:
2 + 6y = 2y2 + -6

Reorder the terms:
2 + 6y = -6 + 2y2

Solving
2 + 6y = -6 + 2y2

Solving for variable 'y'.

Reorder the terms:
2 + 6 + 6y + -2y2 = -6 + 2y2 + 6 + -2y2

Combine like terms: 2 + 6 = 8
8 + 6y + -2y2 = -6 + 2y2 + 6 + -2y2

Reorder the terms:
8 + 6y + -2y2 = -6 + 6 + 2y2 + -2y2

Combine like terms: -6 + 6 = 0
8 + 6y + -2y2 = 0 + 2y2 + -2y2
8 + 6y + -2y2 = 2y2 + -2y2

Combine like terms: 2y2 + -2y2 = 0
8 + 6y + -2y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(4 + 3y + -1y2) = 0

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

Ignore the factor 2.

Subproblem 1

Set the factor '(4 + -1y)' equal to zero and attempt to solve: Simplifying 4 + -1y = 0 Solving 4 + -1y = 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 + -1y = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1y = 0 + -4 -1y = 0 + -4 Combine like terms: 0 + -4 = -4 -1y = -4 Divide each side by '-1'. y = 4 Simplifying y = 4

Subproblem 2

Set the factor '(1 + y)' equal to zero and attempt to solve: Simplifying 1 + y = 0 Solving 1 + y = 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 + y = 0 + -1 Combine like terms: 1 + -1 = 0 0 + y = 0 + -1 y = 0 + -1 Combine like terms: 0 + -1 = -1 y = -1 Simplifying y = -1

Solution

y = {4, -1}

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