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Simplifying 6y2 = -9y + 27 Reorder the terms: 6y2 = 27 + -9y Solving 6y2 = 27 + -9y Solving for variable 'y'. Reorder the terms: -27 + 9y + 6y2 = 27 + -9y + -27 + 9y Reorder the terms: -27 + 9y + 6y2 = 27 + -27 + -9y + 9y Combine like terms: 27 + -27 = 0 -27 + 9y + 6y2 = 0 + -9y + 9y -27 + 9y + 6y2 = -9y + 9y Combine like terms: -9y + 9y = 0 -27 + 9y + 6y2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-9 + 3y + 2y2) = 0 Factor a trinomial. 3((-3 + -1y)(3 + -2y)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-3 + -1y)' equal to zero and attempt to solve: Simplifying -3 + -1y = 0 Solving -3 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1y = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1y = 0 + 3 -1y = 0 + 3 Combine like terms: 0 + 3 = 3 -1y = 3 Divide each side by '-1'. y = -3 Simplifying y = -3Subproblem 2
Set the factor '(3 + -2y)' equal to zero and attempt to solve: Simplifying 3 + -2y = 0 Solving 3 + -2y = 0 Move all terms containing y to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -2y = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2y = 0 + -3 -2y = 0 + -3 Combine like terms: 0 + -3 = -3 -2y = -3 Divide each side by '-2'. y = 1.5 Simplifying y = 1.5Solution
y = {-3, 1.5}
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