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Simplifying 12n2 + -14n + -40 = 0 Reorder the terms: -40 + -14n + 12n2 = 0 Solving -40 + -14n + 12n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '2'. 2(-20 + -7n + 6n2) = 0 Factor a trinomial. 2((-4 + -3n)(5 + -2n)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-4 + -3n)' equal to zero and attempt to solve: Simplifying -4 + -3n = 0 Solving -4 + -3n = 0 Move all terms containing n to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -3n = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -3n = 0 + 4 -3n = 0 + 4 Combine like terms: 0 + 4 = 4 -3n = 4 Divide each side by '-3'. n = -1.333333333 Simplifying n = -1.333333333Subproblem 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 = {-1.333333333, 2.5}
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