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Simplifying 12n2 + -27n + -84 = 0 Reorder the terms: -84 + -27n + 12n2 = 0 Solving -84 + -27n + 12n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '3'. 3(-28 + -9n + 4n2) = 0 Factor a trinomial. 3((-7 + -4n)(4 + -1n)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-7 + -4n)' equal to zero and attempt to solve: Simplifying -7 + -4n = 0 Solving -7 + -4n = 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 + -4n = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -4n = 0 + 7 -4n = 0 + 7 Combine like terms: 0 + 7 = 7 -4n = 7 Divide each side by '-4'. n = -1.75 Simplifying n = -1.75Subproblem 2
Set the factor '(4 + -1n)' equal to zero and attempt to solve: Simplifying 4 + -1n = 0 Solving 4 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1n = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1n = 0 + -4 -1n = 0 + -4 Combine like terms: 0 + -4 = -4 -1n = -4 Divide each side by '-1'. n = 4 Simplifying n = 4Solution
n = {-1.75, 4}
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