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Simplifying (5y + 14)(7y + 6) = 0 Reorder the terms: (14 + 5y)(7y + 6) = 0 Reorder the terms: (14 + 5y)(6 + 7y) = 0 Multiply (14 + 5y) * (6 + 7y) (14(6 + 7y) + 5y * (6 + 7y)) = 0 ((6 * 14 + 7y * 14) + 5y * (6 + 7y)) = 0 ((84 + 98y) + 5y * (6 + 7y)) = 0 (84 + 98y + (6 * 5y + 7y * 5y)) = 0 (84 + 98y + (30y + 35y2)) = 0 Combine like terms: 98y + 30y = 128y (84 + 128y + 35y2) = 0 Solving 84 + 128y + 35y2 = 0 Solving for variable 'y'. Factor a trinomial. (14 + 5y)(6 + 7y) = 0Subproblem 1
Set the factor '(14 + 5y)' equal to zero and attempt to solve: Simplifying 14 + 5y = 0 Solving 14 + 5y = 0 Move all terms containing y to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + 5y = 0 + -14 Combine like terms: 14 + -14 = 0 0 + 5y = 0 + -14 5y = 0 + -14 Combine like terms: 0 + -14 = -14 5y = -14 Divide each side by '5'. y = -2.8 Simplifying y = -2.8Subproblem 2
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 = {-2.8, -0.8571428571}
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