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Simplifying (5n + -1)(7n + -10) = 0 Reorder the terms: (-1 + 5n)(7n + -10) = 0 Reorder the terms: (-1 + 5n)(-10 + 7n) = 0 Multiply (-1 + 5n) * (-10 + 7n) (-1(-10 + 7n) + 5n * (-10 + 7n)) = 0 ((-10 * -1 + 7n * -1) + 5n * (-10 + 7n)) = 0 ((10 + -7n) + 5n * (-10 + 7n)) = 0 (10 + -7n + (-10 * 5n + 7n * 5n)) = 0 (10 + -7n + (-50n + 35n2)) = 0 Combine like terms: -7n + -50n = -57n (10 + -57n + 35n2) = 0 Solving 10 + -57n + 35n2 = 0 Solving for variable 'n'. Factor a trinomial. (1 + -5n)(10 + -7n) = 0Subproblem 1
Set the factor '(1 + -5n)' equal to zero and attempt to solve: Simplifying 1 + -5n = 0 Solving 1 + -5n = 0 Move all terms containing n to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -5n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -5n = 0 + -1 -5n = 0 + -1 Combine like terms: 0 + -1 = -1 -5n = -1 Divide each side by '-5'. n = 0.2 Simplifying n = 0.2Subproblem 2
Set the factor '(10 + -7n)' equal to zero and attempt to solve: Simplifying 10 + -7n = 0 Solving 10 + -7n = 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 + -7n = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -7n = 0 + -10 -7n = 0 + -10 Combine like terms: 0 + -10 = -10 -7n = -10 Divide each side by '-7'. n = 1.428571429 Simplifying n = 1.428571429Solution
n = {0.2, 1.428571429}
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