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Simplifying 40 = 13 + -6y + y2 Solving 40 = 13 + -6y + y2 Solving for variable 'y'. Combine like terms: 40 + -13 = 27 27 + 6y + -1y2 = 13 + -6y + y2 + -13 + 6y + -1y2 Reorder the terms: 27 + 6y + -1y2 = 13 + -13 + -6y + 6y + y2 + -1y2 Combine like terms: 13 + -13 = 0 27 + 6y + -1y2 = 0 + -6y + 6y + y2 + -1y2 27 + 6y + -1y2 = -6y + 6y + y2 + -1y2 Combine like terms: -6y + 6y = 0 27 + 6y + -1y2 = 0 + y2 + -1y2 27 + 6y + -1y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 27 + 6y + -1y2 = 0 Factor a trinomial. (9 + -1y)(3 + y) = 0Subproblem 1
Set the factor '(9 + -1y)' equal to zero and attempt to solve: Simplifying 9 + -1y = 0 Solving 9 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1y = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1y = 0 + -9 -1y = 0 + -9 Combine like terms: 0 + -9 = -9 -1y = -9 Divide each side by '-1'. y = 9 Simplifying y = 9Subproblem 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 = -3Solution
y = {9, -3}
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