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Simplifying 840 = -6n2 + 162n Reorder the terms: 840 = 162n + -6n2 Solving 840 = 162n + -6n2 Solving for variable 'n'. Reorder the terms: 840 + -162n + 6n2 = 162n + -162n + -6n2 + 6n2 Combine like terms: 162n + -162n = 0 840 + -162n + 6n2 = 0 + -6n2 + 6n2 840 + -162n + 6n2 = -6n2 + 6n2 Combine like terms: -6n2 + 6n2 = 0 840 + -162n + 6n2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(140 + -27n + n2) = 0 Factor a trinomial. 6((7 + -1n)(20 + -1n)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(7 + -1n)' equal to zero and attempt to solve: Simplifying 7 + -1n = 0 Solving 7 + -1n = 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 + -1n = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1n = 0 + -7 -1n = 0 + -7 Combine like terms: 0 + -7 = -7 -1n = -7 Divide each side by '-1'. n = 7 Simplifying n = 7Subproblem 2
Set the factor '(20 + -1n)' equal to zero and attempt to solve: Simplifying 20 + -1n = 0 Solving 20 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + -1n = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -1n = 0 + -20 -1n = 0 + -20 Combine like terms: 0 + -20 = -20 -1n = -20 Divide each side by '-1'. n = 20 Simplifying n = 20Solution
n = {7, 20}
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