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Simplifying 9y(2y + 1) = 9 Reorder the terms: 9y(1 + 2y) = 9 (1 * 9y + 2y * 9y) = 9 (9y + 18y2) = 9 Solving 9y + 18y2 = 9 Solving for variable 'y'. Reorder the terms: -9 + 9y + 18y2 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + 9y + 18y2 = 0 Factor out the Greatest Common Factor (GCF), '9'. 9(-1 + y + 2y2) = 0 Factor a trinomial. 9((-1 + -1y)(1 + -2y)) = 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 '(1 + -2y)' equal to zero and attempt to solve: Simplifying 1 + -2y = 0 Solving 1 + -2y = 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 + -2y = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2y = 0 + -1 -2y = 0 + -1 Combine like terms: 0 + -1 = -1 -2y = -1 Divide each side by '-2'. y = 0.5 Simplifying y = 0.5Solution
y = {-1, 0.5}
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