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Simplifying 12n2 = -42n + -30 Reorder the terms: 12n2 = -30 + -42n Solving 12n2 = -30 + -42n Solving for variable 'n'. Reorder the terms: 30 + 42n + 12n2 = -30 + -42n + 30 + 42n Reorder the terms: 30 + 42n + 12n2 = -30 + 30 + -42n + 42n Combine like terms: -30 + 30 = 0 30 + 42n + 12n2 = 0 + -42n + 42n 30 + 42n + 12n2 = -42n + 42n Combine like terms: -42n + 42n = 0 30 + 42n + 12n2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(5 + 7n + 2n2) = 0 Factor a trinomial. 6((5 + 2n)(1 + n)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(5 + 2n)' equal to zero and attempt to solve: Simplifying 5 + 2n = 0 Solving 5 + 2n = 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 + 2n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2n = 0 + -5 2n = 0 + -5 Combine like terms: 0 + -5 = -5 2n = -5 Divide each side by '2'. n = -2.5 Simplifying n = -2.5Subproblem 2
Set the factor '(1 + n)' equal to zero and attempt to solve: Simplifying 1 + n = 0 Solving 1 + n = 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 + n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + n = 0 + -1 n = 0 + -1 Combine like terms: 0 + -1 = -1 n = -1 Simplifying n = -1Solution
n = {-2.5, -1}
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