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Simplifying -35n2 + 145n + -120 = 0 Reorder the terms: -120 + 145n + -35n2 = 0 Solving -120 + 145n + -35n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '5'. 5(-24 + 29n + -7n2) = 0 Factor a trinomial. 5((-3 + n)(8 + -7n)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-3 + n)' equal to zero and attempt to solve: Simplifying -3 + n = 0 Solving -3 + n = 0 Move all terms containing n to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + n = 0 + 3 Combine like terms: -3 + 3 = 0 0 + n = 0 + 3 n = 0 + 3 Combine like terms: 0 + 3 = 3 n = 3 Simplifying n = 3Subproblem 2
Set the factor '(8 + -7n)' equal to zero and attempt to solve: Simplifying 8 + -7n = 0 Solving 8 + -7n = 0 Move all terms containing n to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -7n = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -7n = 0 + -8 -7n = 0 + -8 Combine like terms: 0 + -8 = -8 -7n = -8 Divide each side by '-7'. n = 1.142857143 Simplifying n = 1.142857143Solution
n = {3, 1.142857143}
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