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Simplifying (6y + 9)(7y + 4) = 0 Reorder the terms: (9 + 6y)(7y + 4) = 0 Reorder the terms: (9 + 6y)(4 + 7y) = 0 Multiply (9 + 6y) * (4 + 7y) (9(4 + 7y) + 6y * (4 + 7y)) = 0 ((4 * 9 + 7y * 9) + 6y * (4 + 7y)) = 0 ((36 + 63y) + 6y * (4 + 7y)) = 0 (36 + 63y + (4 * 6y + 7y * 6y)) = 0 (36 + 63y + (24y + 42y2)) = 0 Combine like terms: 63y + 24y = 87y (36 + 87y + 42y2) = 0 Solving 36 + 87y + 42y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '3'. 3(12 + 29y + 14y2) = 0 Factor a trinomial. 3((3 + 2y)(4 + 7y)) = 0 Ignore the factor 3.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 '(4 + 7y)' equal to zero and attempt to solve: Simplifying 4 + 7y = 0 Solving 4 + 7y = 0 Move all terms containing y to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + 7y = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 7y = 0 + -4 7y = 0 + -4 Combine like terms: 0 + -4 = -4 7y = -4 Divide each side by '7'. y = -0.5714285714 Simplifying y = -0.5714285714Solution
y = {-1.5, -0.5714285714}
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