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Simplifying 12n2 + 70n + 100 = 0 Reorder the terms: 100 + 70n + 12n2 = 0 Solving 100 + 70n + 12n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '2'. 2(50 + 35n + 6n2) = 0 Factor a trinomial. 2((10 + 3n)(5 + 2n)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(10 + 3n)' equal to zero and attempt to solve: Simplifying 10 + 3n = 0 Solving 10 + 3n = 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 + 3n = 0 + -10 Combine like terms: 10 + -10 = 0 0 + 3n = 0 + -10 3n = 0 + -10 Combine like terms: 0 + -10 = -10 3n = -10 Divide each side by '3'. n = -3.333333333 Simplifying n = -3.333333333Subproblem 2
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 = -2.5Solution
n = {-3.333333333, -2.5}
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