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Simplifying (y + 1)(y + 2) = 30 Reorder the terms: (1 + y)(y + 2) = 30 Reorder the terms: (1 + y)(2 + y) = 30 Multiply (1 + y) * (2 + y) (1(2 + y) + y(2 + y)) = 30 ((2 * 1 + y * 1) + y(2 + y)) = 30 ((2 + 1y) + y(2 + y)) = 30 (2 + 1y + (2 * y + y * y)) = 30 (2 + 1y + (2y + y2)) = 30 Combine like terms: 1y + 2y = 3y (2 + 3y + y2) = 30 Solving 2 + 3y + y2 = 30 Solving for variable 'y'. Reorder the terms: 2 + -30 + 3y + y2 = 30 + -30 Combine like terms: 2 + -30 = -28 -28 + 3y + y2 = 30 + -30 Combine like terms: 30 + -30 = 0 -28 + 3y + y2 = 0 Factor a trinomial. (-7 + -1y)(4 + -1y) = 0Subproblem 1
Set the factor '(-7 + -1y)' equal to zero and attempt to solve: Simplifying -7 + -1y = 0 Solving -7 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -1y = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1y = 0 + 7 -1y = 0 + 7 Combine like terms: 0 + 7 = 7 -1y = 7 Divide each side by '-1'. y = -7 Simplifying y = -7Subproblem 2
Set the factor '(4 + -1y)' equal to zero and attempt to solve: Simplifying 4 + -1y = 0 Solving 4 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1y = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1y = 0 + -4 -1y = 0 + -4 Combine like terms: 0 + -4 = -4 -1y = -4 Divide each side by '-1'. y = 4 Simplifying y = 4Solution
y = {-7, 4}
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