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Simplifying 9(6y + -5)(2y + 3) = 0 Reorder the terms: 9(-5 + 6y)(2y + 3) = 0 Reorder the terms: 9(-5 + 6y)(3 + 2y) = 0 Multiply (-5 + 6y) * (3 + 2y) 9(-5(3 + 2y) + 6y * (3 + 2y)) = 0 9((3 * -5 + 2y * -5) + 6y * (3 + 2y)) = 0 9((-15 + -10y) + 6y * (3 + 2y)) = 0 9(-15 + -10y + (3 * 6y + 2y * 6y)) = 0 9(-15 + -10y + (18y + 12y2)) = 0 Combine like terms: -10y + 18y = 8y 9(-15 + 8y + 12y2) = 0 (-15 * 9 + 8y * 9 + 12y2 * 9) = 0 (-135 + 72y + 108y2) = 0 Solving -135 + 72y + 108y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '9'. 9(-15 + 8y + 12y2) = 0 Factor a trinomial. 9((-3 + -2y)(5 + -6y)) = 0 Ignore the factor 9.Subproblem 1
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 = -1.5Subproblem 2
Set the factor '(5 + -6y)' equal to zero and attempt to solve: Simplifying 5 + -6y = 0 Solving 5 + -6y = 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 + -6y = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -6y = 0 + -5 -6y = 0 + -5 Combine like terms: 0 + -5 = -5 -6y = -5 Divide each side by '-6'. y = 0.8333333333 Simplifying y = 0.8333333333Solution
y = {-1.5, 0.8333333333}
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