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Simplifying y2 + -12y + 36 = 2y2 + -13y + 30 Reorder the terms: 36 + -12y + y2 = 2y2 + -13y + 30 Reorder the terms: 36 + -12y + y2 = 30 + -13y + 2y2 Solving 36 + -12y + y2 = 30 + -13y + 2y2 Solving for variable 'y'. Reorder the terms: 36 + -30 + -12y + 13y + y2 + -2y2 = 30 + -13y + 2y2 + -30 + 13y + -2y2 Combine like terms: 36 + -30 = 6 6 + -12y + 13y + y2 + -2y2 = 30 + -13y + 2y2 + -30 + 13y + -2y2 Combine like terms: -12y + 13y = 1y 6 + 1y + y2 + -2y2 = 30 + -13y + 2y2 + -30 + 13y + -2y2 Combine like terms: y2 + -2y2 = -1y2 6 + 1y + -1y2 = 30 + -13y + 2y2 + -30 + 13y + -2y2 Reorder the terms: 6 + 1y + -1y2 = 30 + -30 + -13y + 13y + 2y2 + -2y2 Combine like terms: 30 + -30 = 0 6 + 1y + -1y2 = 0 + -13y + 13y + 2y2 + -2y2 6 + 1y + -1y2 = -13y + 13y + 2y2 + -2y2 Combine like terms: -13y + 13y = 0 6 + 1y + -1y2 = 0 + 2y2 + -2y2 6 + 1y + -1y2 = 2y2 + -2y2 Combine like terms: 2y2 + -2y2 = 0 6 + 1y + -1y2 = 0 Factor a trinomial. (3 + -1y)(2 + y) = 0Subproblem 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 = 3Subproblem 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 = {3, -2}
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