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Simplifying (y + -3)(y + -4) = 30 Reorder the terms: (-3 + y)(y + -4) = 30 Reorder the terms: (-3 + y)(-4 + y) = 30 Multiply (-3 + y) * (-4 + y) (-3(-4 + y) + y(-4 + y)) = 30 ((-4 * -3 + y * -3) + y(-4 + y)) = 30 ((12 + -3y) + y(-4 + y)) = 30 (12 + -3y + (-4 * y + y * y)) = 30 (12 + -3y + (-4y + y2)) = 30 Combine like terms: -3y + -4y = -7y (12 + -7y + y2) = 30 Solving 12 + -7y + y2 = 30 Solving for variable 'y'. Reorder the terms: 12 + -30 + -7y + y2 = 30 + -30 Combine like terms: 12 + -30 = -18 -18 + -7y + y2 = 30 + -30 Combine like terms: 30 + -30 = 0 -18 + -7y + y2 = 0 Factor a trinomial. (-2 + -1y)(9 + -1y) = 0Subproblem 1
Set the factor '(-2 + -1y)' equal to zero and attempt to solve: Simplifying -2 + -1y = 0 Solving -2 + -1y = 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 + -1y = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1y = 0 + 2 -1y = 0 + 2 Combine like terms: 0 + 2 = 2 -1y = 2 Divide each side by '-1'. y = -2 Simplifying y = -2Subproblem 2
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 = 9Solution
y = {-2, 9}
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