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Simplifying 18n2 + -72n + 40 = 0 Reorder the terms: 40 + -72n + 18n2 = 0 Solving 40 + -72n + 18n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '2'. 2(20 + -36n + 9n2) = 0 Factor a trinomial. 2((2 + -3n)(10 + -3n)) = 0 Ignore the factor 2.Subproblem 1
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 = 0.6666666667Subproblem 2
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 = 3.333333333Solution
n = {0.6666666667, 3.333333333}
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