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Simplifying y(5y + 7)(7y + 6) = 0 Reorder the terms: y(7 + 5y)(7y + 6) = 0 Reorder the terms: y(7 + 5y)(6 + 7y) = 0 Multiply (7 + 5y) * (6 + 7y) y(7(6 + 7y) + 5y * (6 + 7y)) = 0 y((6 * 7 + 7y * 7) + 5y * (6 + 7y)) = 0 y((42 + 49y) + 5y * (6 + 7y)) = 0 y(42 + 49y + (6 * 5y + 7y * 5y)) = 0 y(42 + 49y + (30y + 35y2)) = 0 Combine like terms: 49y + 30y = 79y y(42 + 79y + 35y2) = 0 (42 * y + 79y * y + 35y2 * y) = 0 (42y + 79y2 + 35y3) = 0 Solving 42y + 79y2 + 35y3 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), 'y'. y(42 + 79y + 35y2) = 0 Factor a trinomial. y((7 + 5y)(6 + 7y)) = 0Subproblem 1
Set the factor 'y' equal to zero and attempt to solve: Simplifying y = 0 Solving y = 0 Move all terms containing y to the left, all other terms to the right. Simplifying y = 0Subproblem 2
Set the factor '(7 + 5y)' equal to zero and attempt to solve: Simplifying 7 + 5y = 0 Solving 7 + 5y = 0 Move all terms containing y to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 5y = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 5y = 0 + -7 5y = 0 + -7 Combine like terms: 0 + -7 = -7 5y = -7 Divide each side by '5'. y = -1.4 Simplifying y = -1.4Subproblem 3
Set the factor '(6 + 7y)' equal to zero and attempt to solve: Simplifying 6 + 7y = 0 Solving 6 + 7y = 0 Move all terms containing y to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + 7y = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 7y = 0 + -6 7y = 0 + -6 Combine like terms: 0 + -6 = -6 7y = -6 Divide each side by '7'. y = -0.8571428571 Simplifying y = -0.8571428571Solution
y = {0, -1.4, -0.8571428571}
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