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Simplifying (y + 8)(y + -9) = -52 Reorder the terms: (8 + y)(y + -9) = -52 Reorder the terms: (8 + y)(-9 + y) = -52 Multiply (8 + y) * (-9 + y) (8(-9 + y) + y(-9 + y)) = -52 ((-9 * 8 + y * 8) + y(-9 + y)) = -52 ((-72 + 8y) + y(-9 + y)) = -52 (-72 + 8y + (-9 * y + y * y)) = -52 (-72 + 8y + (-9y + y2)) = -52 Combine like terms: 8y + -9y = -1y (-72 + -1y + y2) = -52 Solving -72 + -1y + y2 = -52 Solving for variable 'y'. Reorder the terms: -72 + 52 + -1y + y2 = -52 + 52 Combine like terms: -72 + 52 = -20 -20 + -1y + y2 = -52 + 52 Combine like terms: -52 + 52 = 0 -20 + -1y + y2 = 0 Factor a trinomial. (-4 + -1y)(5 + -1y) = 0Subproblem 1
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 = -4Subproblem 2
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 = 5Solution
y = {-4, 5}
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