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Simplifying (5n + 7)(n + 10) = 0 Reorder the terms: (7 + 5n)(n + 10) = 0 Reorder the terms: (7 + 5n)(10 + n) = 0 Multiply (7 + 5n) * (10 + n) (7(10 + n) + 5n * (10 + n)) = 0 ((10 * 7 + n * 7) + 5n * (10 + n)) = 0 ((70 + 7n) + 5n * (10 + n)) = 0 (70 + 7n + (10 * 5n + n * 5n)) = 0 (70 + 7n + (50n + 5n2)) = 0 Combine like terms: 7n + 50n = 57n (70 + 57n + 5n2) = 0 Solving 70 + 57n + 5n2 = 0 Solving for variable 'n'. Factor a trinomial. (10 + n)(7 + 5n) = 0Subproblem 1
Set the factor '(10 + n)' equal to zero and attempt to solve: Simplifying 10 + n = 0 Solving 10 + n = 0 Move all terms containing n to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + n = 0 + -10 Combine like terms: 10 + -10 = 0 0 + n = 0 + -10 n = 0 + -10 Combine like terms: 0 + -10 = -10 n = -10 Simplifying n = -10Subproblem 2
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 = -1.4Solution
n = {-10, -1.4}
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