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Simplifying 0 = 9y2 + -54y + 45 Reorder the terms: 0 = 45 + -54y + 9y2 Solving 0 = 45 + -54y + 9y2 Solving for variable 'y'. Combine like terms: 0 + -45 = -45 -45 + 54y + -9y2 = 45 + -54y + 9y2 + -45 + 54y + -9y2 Reorder the terms: -45 + 54y + -9y2 = 45 + -45 + -54y + 54y + 9y2 + -9y2 Combine like terms: 45 + -45 = 0 -45 + 54y + -9y2 = 0 + -54y + 54y + 9y2 + -9y2 -45 + 54y + -9y2 = -54y + 54y + 9y2 + -9y2 Combine like terms: -54y + 54y = 0 -45 + 54y + -9y2 = 0 + 9y2 + -9y2 -45 + 54y + -9y2 = 9y2 + -9y2 Combine like terms: 9y2 + -9y2 = 0 -45 + 54y + -9y2 = 0 Factor out the Greatest Common Factor (GCF), '9'. 9(-5 + 6y + -1y2) = 0 Factor a trinomial. 9((-5 + y)(1 + -1y)) = 0 Ignore the factor 9.Subproblem 1
Set the factor '(-5 + y)' equal to zero and attempt to solve: Simplifying -5 + y = 0 Solving -5 + y = 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 + y = 0 + 5 Combine like terms: -5 + 5 = 0 0 + y = 0 + 5 y = 0 + 5 Combine like terms: 0 + 5 = 5 y = 5 Simplifying y = 5Subproblem 2
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 = 1Solution
y = {5, 1}
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