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Simplifying 10n2 = 270 + 60n Solving 10n2 = 270 + 60n Solving for variable 'n'. Reorder the terms: -270 + -60n + 10n2 = 270 + 60n + -270 + -60n Reorder the terms: -270 + -60n + 10n2 = 270 + -270 + 60n + -60n Combine like terms: 270 + -270 = 0 -270 + -60n + 10n2 = 0 + 60n + -60n -270 + -60n + 10n2 = 60n + -60n Combine like terms: 60n + -60n = 0 -270 + -60n + 10n2 = 0 Factor out the Greatest Common Factor (GCF), '10'. 10(-27 + -6n + n2) = 0 Factor a trinomial. 10((-3 + -1n)(9 + -1n)) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(-3 + -1n)' equal to zero and attempt to solve: Simplifying -3 + -1n = 0 Solving -3 + -1n = 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 + -1n = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1n = 0 + 3 -1n = 0 + 3 Combine like terms: 0 + 3 = 3 -1n = 3 Divide each side by '-1'. n = -3 Simplifying n = -3Subproblem 2
Set the factor '(9 + -1n)' equal to zero and attempt to solve: Simplifying 9 + -1n = 0 Solving 9 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1n = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1n = 0 + -9 -1n = 0 + -9 Combine like terms: 0 + -9 = -9 -1n = -9 Divide each side by '-1'. n = 9 Simplifying n = 9Solution
n = {-3, 9}
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