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Simplifying 5(y + 9)(-1y + 1) = 0 Reorder the terms: 5(9 + y)(-1y + 1) = 0 Reorder the terms: 5(9 + y)(1 + -1y) = 0 Multiply (9 + y) * (1 + -1y) 5(9(1 + -1y) + y(1 + -1y)) = 0 5((1 * 9 + -1y * 9) + y(1 + -1y)) = 0 5((9 + -9y) + y(1 + -1y)) = 0 5(9 + -9y + (1 * y + -1y * y)) = 0 5(9 + -9y + (1y + -1y2)) = 0 Combine like terms: -9y + 1y = -8y 5(9 + -8y + -1y2) = 0 (9 * 5 + -8y * 5 + -1y2 * 5) = 0 (45 + -40y + -5y2) = 0 Solving 45 + -40y + -5y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '5'. 5(9 + -8y + -1y2) = 0 Factor a trinomial. 5((1 + -1y)(9 + y)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(1 + -1y)' equal to zero and attempt to solve: Simplifying 1 + -1y = 0 Solving 1 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1y = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1y = 0 + -1 -1y = 0 + -1 Combine like terms: 0 + -1 = -1 -1y = -1 Divide each side by '-1'. y = 1 Simplifying y = 1Subproblem 2
Set the factor '(9 + y)' equal to zero and attempt to solve: Simplifying 9 + y = 0 Solving 9 + y = 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 + y = 0 + -9 Combine like terms: 9 + -9 = 0 0 + y = 0 + -9 y = 0 + -9 Combine like terms: 0 + -9 = -9 y = -9 Simplifying y = -9Solution
y = {1, -9}
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