y^2+2y+11=-6y-4

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Solution for y^2+2y+11=-6y-4 equation:


Simplifying
y2 + 2y + 11 = -6y + -4

Reorder the terms:
11 + 2y + y2 = -6y + -4

Reorder the terms:
11 + 2y + y2 = -4 + -6y

Solving
11 + 2y + y2 = -4 + -6y

Solving for variable 'y'.

Reorder the terms:
11 + 4 + 2y + 6y + y2 = -4 + -6y + 4 + 6y

Combine like terms: 11 + 4 = 15
15 + 2y + 6y + y2 = -4 + -6y + 4 + 6y

Combine like terms: 2y + 6y = 8y
15 + 8y + y2 = -4 + -6y + 4 + 6y

Reorder the terms:
15 + 8y + y2 = -4 + 4 + -6y + 6y

Combine like terms: -4 + 4 = 0
15 + 8y + y2 = 0 + -6y + 6y
15 + 8y + y2 = -6y + 6y

Combine like terms: -6y + 6y = 0
15 + 8y + y2 = 0

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

Subproblem 1

Set the factor '(5 + y)' equal to zero and attempt to solve: Simplifying 5 + y = 0 Solving 5 + y = 0 Move all terms containing y to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + y = 0 + -5 Combine like terms: 5 + -5 = 0 0 + y = 0 + -5 y = 0 + -5 Combine like terms: 0 + -5 = -5 y = -5 Simplifying y = -5

Subproblem 2

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

Solution

y = {-5, -3}

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