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Simplifying y2 + y + 13 = -6y + 3 Reorder the terms: 13 + y + y2 = -6y + 3 Reorder the terms: 13 + y + y2 = 3 + -6y Solving 13 + y + y2 = 3 + -6y Solving for variable 'y'. Reorder the terms: 13 + -3 + y + 6y + y2 = 3 + -6y + -3 + 6y Combine like terms: 13 + -3 = 10 10 + y + 6y + y2 = 3 + -6y + -3 + 6y Combine like terms: y + 6y = 7y 10 + 7y + y2 = 3 + -6y + -3 + 6y Reorder the terms: 10 + 7y + y2 = 3 + -3 + -6y + 6y Combine like terms: 3 + -3 = 0 10 + 7y + y2 = 0 + -6y + 6y 10 + 7y + y2 = -6y + 6y Combine like terms: -6y + 6y = 0 10 + 7y + y2 = 0 Factor a trinomial. (5 + y)(2 + y) = 0Subproblem 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 = -5Subproblem 2
Set the factor '(2 + y)' equal to zero and attempt to solve: Simplifying 2 + y = 0 Solving 2 + y = 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 + y = 0 + -2 Combine like terms: 2 + -2 = 0 0 + y = 0 + -2 y = 0 + -2 Combine like terms: 0 + -2 = -2 y = -2 Simplifying y = -2Solution
y = {-5, -2}
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