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Simplifying 24n2 + -40n + 14 = 0 Reorder the terms: 14 + -40n + 24n2 = 0 Solving 14 + -40n + 24n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '2'. 2(7 + -20n + 12n2) = 0 Factor a trinomial. 2((1 + -2n)(7 + -6n)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + -2n)' equal to zero and attempt to solve: Simplifying 1 + -2n = 0 Solving 1 + -2n = 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 + -2n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2n = 0 + -1 -2n = 0 + -1 Combine like terms: 0 + -1 = -1 -2n = -1 Divide each side by '-2'. n = 0.5 Simplifying n = 0.5Subproblem 2
Set the factor '(7 + -6n)' equal to zero and attempt to solve: Simplifying 7 + -6n = 0 Solving 7 + -6n = 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 + -6n = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -6n = 0 + -7 -6n = 0 + -7 Combine like terms: 0 + -7 = -7 -6n = -7 Divide each side by '-6'. n = 1.166666667 Simplifying n = 1.166666667Solution
n = {0.5, 1.166666667}
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