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Simplifying 140n2 + 124n + -160 = 0 Reorder the terms: -160 + 124n + 140n2 = 0 Solving -160 + 124n + 140n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '4'. 4(-40 + 31n + 35n2) = 0 Factor a trinomial. 4((-8 + -5n)(5 + -7n)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-8 + -5n)' equal to zero and attempt to solve: Simplifying -8 + -5n = 0 Solving -8 + -5n = 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 + -5n = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -5n = 0 + 8 -5n = 0 + 8 Combine like terms: 0 + 8 = 8 -5n = 8 Divide each side by '-5'. n = -1.6 Simplifying n = -1.6Subproblem 2
Set the factor '(5 + -7n)' equal to zero and attempt to solve: Simplifying 5 + -7n = 0 Solving 5 + -7n = 0 Move all terms containing n to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -7n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -7n = 0 + -5 -7n = 0 + -5 Combine like terms: 0 + -5 = -5 -7n = -5 Divide each side by '-7'. n = 0.7142857143 Simplifying n = 0.7142857143Solution
n = {-1.6, 0.7142857143}
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