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Simplifying 48n2 + 108n + -210 = 0 Reorder the terms: -210 + 108n + 48n2 = 0 Solving -210 + 108n + 48n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '6'. 6(-35 + 18n + 8n2) = 0 Factor a trinomial. 6((-7 + -2n)(5 + -4n)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-7 + -2n)' equal to zero and attempt to solve: Simplifying -7 + -2n = 0 Solving -7 + -2n = 0 Move all terms containing n to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -2n = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -2n = 0 + 7 -2n = 0 + 7 Combine like terms: 0 + 7 = 7 -2n = 7 Divide each side by '-2'. n = -3.5 Simplifying n = -3.5Subproblem 2
Set the factor '(5 + -4n)' equal to zero and attempt to solve: Simplifying 5 + -4n = 0 Solving 5 + -4n = 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 + -4n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4n = 0 + -5 -4n = 0 + -5 Combine like terms: 0 + -5 = -5 -4n = -5 Divide each side by '-4'. n = 1.25 Simplifying n = 1.25Solution
n = {-3.5, 1.25}
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