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Simplifying 192 = 1200 + 12n + -6n2 Solving 192 = 1200 + 12n + -6n2 Solving for variable 'n'. Combine like terms: 192 + -1200 = -1008 -1008 + -12n + 6n2 = 1200 + 12n + -6n2 + -1200 + -12n + 6n2 Reorder the terms: -1008 + -12n + 6n2 = 1200 + -1200 + 12n + -12n + -6n2 + 6n2 Combine like terms: 1200 + -1200 = 0 -1008 + -12n + 6n2 = 0 + 12n + -12n + -6n2 + 6n2 -1008 + -12n + 6n2 = 12n + -12n + -6n2 + 6n2 Combine like terms: 12n + -12n = 0 -1008 + -12n + 6n2 = 0 + -6n2 + 6n2 -1008 + -12n + 6n2 = -6n2 + 6n2 Combine like terms: -6n2 + 6n2 = 0 -1008 + -12n + 6n2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-168 + -2n + n2) = 0 Factor a trinomial. 6((-12 + -1n)(14 + -1n)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-12 + -1n)' equal to zero and attempt to solve: Simplifying -12 + -1n = 0 Solving -12 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + -1n = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -1n = 0 + 12 -1n = 0 + 12 Combine like terms: 0 + 12 = 12 -1n = 12 Divide each side by '-1'. n = -12 Simplifying n = -12Subproblem 2
Set the factor '(14 + -1n)' equal to zero and attempt to solve: Simplifying 14 + -1n = 0 Solving 14 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + -1n = 0 + -14 Combine like terms: 14 + -14 = 0 0 + -1n = 0 + -14 -1n = 0 + -14 Combine like terms: 0 + -14 = -14 -1n = -14 Divide each side by '-1'. n = 14 Simplifying n = 14Solution
n = {-12, 14}
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