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Simplifying (6y + -5)(3y + 9) = 0 Reorder the terms: (-5 + 6y)(3y + 9) = 0 Reorder the terms: (-5 + 6y)(9 + 3y) = 0 Multiply (-5 + 6y) * (9 + 3y) (-5(9 + 3y) + 6y * (9 + 3y)) = 0 ((9 * -5 + 3y * -5) + 6y * (9 + 3y)) = 0 ((-45 + -15y) + 6y * (9 + 3y)) = 0 (-45 + -15y + (9 * 6y + 3y * 6y)) = 0 (-45 + -15y + (54y + 18y2)) = 0 Combine like terms: -15y + 54y = 39y (-45 + 39y + 18y2) = 0 Solving -45 + 39y + 18y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '3'. 3(-15 + 13y + 6y2) = 0 Factor a trinomial. 3((-3 + -1y)(5 + -6y)) = 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 '(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 = {-3, 0.8333333333}
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