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Simplifying 24n2 + 2n + -12 = 0 Reorder the terms: -12 + 2n + 24n2 = 0 Solving -12 + 2n + 24n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '2'. 2(-6 + n + 12n2) = 0 Factor a trinomial. 2((-3 + -4n)(2 + -3n)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + -4n)' equal to zero and attempt to solve: Simplifying -3 + -4n = 0 Solving -3 + -4n = 0 Move all terms containing n to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -4n = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -4n = 0 + 3 -4n = 0 + 3 Combine like terms: 0 + 3 = 3 -4n = 3 Divide each side by '-4'. n = -0.75 Simplifying n = -0.75Subproblem 2
Set the factor '(2 + -3n)' equal to zero and attempt to solve: Simplifying 2 + -3n = 0 Solving 2 + -3n = 0 Move all terms containing n to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -3n = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3n = 0 + -2 -3n = 0 + -2 Combine like terms: 0 + -2 = -2 -3n = -2 Divide each side by '-3'. n = 0.6666666667 Simplifying n = 0.6666666667Solution
n = {-0.75, 0.6666666667}
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