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Simplifying 180n = -108 + -75n2 Solving 180n = -108 + -75n2 Solving for variable 'n'. Reorder the terms: 108 + 180n + 75n2 = -108 + -75n2 + 108 + 75n2 Reorder the terms: 108 + 180n + 75n2 = -108 + 108 + -75n2 + 75n2 Combine like terms: -108 + 108 = 0 108 + 180n + 75n2 = 0 + -75n2 + 75n2 108 + 180n + 75n2 = -75n2 + 75n2 Combine like terms: -75n2 + 75n2 = 0 108 + 180n + 75n2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(36 + 60n + 25n2) = 0 Factor a trinomial. 3((6 + 5n)(6 + 5n)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(6 + 5n)' equal to zero and attempt to solve: Simplifying 6 + 5n = 0 Solving 6 + 5n = 0 Move all terms containing n to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + 5n = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 5n = 0 + -6 5n = 0 + -6 Combine like terms: 0 + -6 = -6 5n = -6 Divide each side by '5'. n = -1.2 Simplifying n = -1.2Subproblem 2
Set the factor '(6 + 5n)' equal to zero and attempt to solve: Simplifying 6 + 5n = 0 Solving 6 + 5n = 0 Move all terms containing n to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + 5n = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 5n = 0 + -6 5n = 0 + -6 Combine like terms: 0 + -6 = -6 5n = -6 Divide each side by '5'. n = -1.2 Simplifying n = -1.2Solution
n = {-1.2, -1.2}
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