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Simplifying (5n + 7)(7n + 2) = 0 Reorder the terms: (7 + 5n)(7n + 2) = 0 Reorder the terms: (7 + 5n)(2 + 7n) = 0 Multiply (7 + 5n) * (2 + 7n) (7(2 + 7n) + 5n * (2 + 7n)) = 0 ((2 * 7 + 7n * 7) + 5n * (2 + 7n)) = 0 ((14 + 49n) + 5n * (2 + 7n)) = 0 (14 + 49n + (2 * 5n + 7n * 5n)) = 0 (14 + 49n + (10n + 35n2)) = 0 Combine like terms: 49n + 10n = 59n (14 + 59n + 35n2) = 0 Solving 14 + 59n + 35n2 = 0 Solving for variable 'n'. Factor a trinomial. (7 + 5n)(2 + 7n) = 0Subproblem 1
Set the factor '(7 + 5n)' equal to zero and attempt to solve: Simplifying 7 + 5n = 0 Solving 7 + 5n = 0 Move all terms containing n to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 5n = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 5n = 0 + -7 5n = 0 + -7 Combine like terms: 0 + -7 = -7 5n = -7 Divide each side by '5'. n = -1.4 Simplifying n = -1.4Subproblem 2
Set the factor '(2 + 7n)' equal to zero and attempt to solve: Simplifying 2 + 7n = 0 Solving 2 + 7n = 0 Move all terms containing n to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 7n = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 7n = 0 + -2 7n = 0 + -2 Combine like terms: 0 + -2 = -2 7n = -2 Divide each side by '7'. n = -0.2857142857 Simplifying n = -0.2857142857Solution
n = {-1.4, -0.2857142857}
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