2y+2y^2+2=14

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Solution for 2y+2y^2+2=14 equation:


Simplifying
2y + 2y2 + 2 = 14

Reorder the terms:
2 + 2y + 2y2 = 14

Solving
2 + 2y + 2y2 = 14

Solving for variable 'y'.

Reorder the terms:
2 + -14 + 2y + 2y2 = 14 + -14

Combine like terms: 2 + -14 = -12
-12 + 2y + 2y2 = 14 + -14

Combine like terms: 14 + -14 = 0
-12 + 2y + 2y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + y + y2) = 0

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

Ignore the factor 2.

Subproblem 1

Set the factor '(-3 + -1y)' equal to zero and attempt to solve: Simplifying -3 + -1y = 0 Solving -3 + -1y = 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 + -1y = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1y = 0 + 3 -1y = 0 + 3 Combine like terms: 0 + 3 = 3 -1y = 3 Divide each side by '-1'. y = -3 Simplifying y = -3

Subproblem 2

Set the factor '(2 + -1y)' equal to zero and attempt to solve: Simplifying 2 + -1y = 0 Solving 2 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1y = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1y = 0 + -2 -1y = 0 + -2 Combine like terms: 0 + -2 = -2 -1y = -2 Divide each side by '-1'. y = 2 Simplifying y = 2

Solution

y = {-3, 2}

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