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Simplifying 81(1 + -1y) + -9(1 + -1y) * y = 0 (1 * 81 + -1y * 81) + -9(1 + -1y) * y = 0 (81 + -81y) + -9(1 + -1y) * y = 0 Reorder the terms for easier multiplication: 81 + -81y + -9y(1 + -1y) = 0 81 + -81y + (1 * -9y + -1y * -9y) = 0 81 + -81y + (-9y + 9y2) = 0 Combine like terms: -81y + -9y = -90y 81 + -90y + 9y2 = 0 Solving 81 + -90y + 9y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '9'. 9(9 + -10y + y2) = 0 Factor a trinomial. 9((1 + -1y)(9 + -1y)) = 0 Ignore the factor 9.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 + -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 = {1, 9}
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