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Simplifying 0 = y2 + y + -30 Reorder the terms: 0 = -30 + y + y2 Solving 0 = -30 + y + y2 Solving for variable 'y'. Combine like terms: 0 + 30 = 30 30 + -1y + -1y2 = -30 + y + y2 + 30 + -1y + -1y2 Reorder the terms: 30 + -1y + -1y2 = -30 + 30 + y + -1y + y2 + -1y2 Combine like terms: -30 + 30 = 0 30 + -1y + -1y2 = 0 + y + -1y + y2 + -1y2 30 + -1y + -1y2 = y + -1y + y2 + -1y2 Combine like terms: y + -1y = 0 30 + -1y + -1y2 = 0 + y2 + -1y2 30 + -1y + -1y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 30 + -1y + -1y2 = 0 Factor a trinomial. (5 + -1y)(6 + y) = 0Subproblem 1
Set the factor '(5 + -1y)' equal to zero and attempt to solve: Simplifying 5 + -1y = 0 Solving 5 + -1y = 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 + -1y = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1y = 0 + -5 -1y = 0 + -5 Combine like terms: 0 + -5 = -5 -1y = -5 Divide each side by '-1'. y = 5 Simplifying y = 5Subproblem 2
Set the factor '(6 + y)' equal to zero and attempt to solve: Simplifying 6 + y = 0 Solving 6 + y = 0 Move all terms containing y to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + y = 0 + -6 Combine like terms: 6 + -6 = 0 0 + y = 0 + -6 y = 0 + -6 Combine like terms: 0 + -6 = -6 y = -6 Simplifying y = -6Solution
y = {5, -6}
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