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Simplifying 10n2 + 130n + -10800 = 0 Reorder the terms: -10800 + 130n + 10n2 = 0 Solving -10800 + 130n + 10n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '10'. 10(-1080 + 13n + n2) = 0 Factor a trinomial. 10((-40 + -1n)(27 + -1n)) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(-40 + -1n)' equal to zero and attempt to solve: Simplifying -40 + -1n = 0 Solving -40 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '40' to each side of the equation. -40 + 40 + -1n = 0 + 40 Combine like terms: -40 + 40 = 0 0 + -1n = 0 + 40 -1n = 0 + 40 Combine like terms: 0 + 40 = 40 -1n = 40 Divide each side by '-1'. n = -40 Simplifying n = -40Subproblem 2
Set the factor '(27 + -1n)' equal to zero and attempt to solve: Simplifying 27 + -1n = 0 Solving 27 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-27' to each side of the equation. 27 + -27 + -1n = 0 + -27 Combine like terms: 27 + -27 = 0 0 + -1n = 0 + -27 -1n = 0 + -27 Combine like terms: 0 + -27 = -27 -1n = -27 Divide each side by '-1'. n = 27 Simplifying n = 27Solution
n = {-40, 27}
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