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Simplifying 16n2 + 68n + -168 = 0 Reorder the terms: -168 + 68n + 16n2 = 0 Solving -168 + 68n + 16n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '4'. 4(-42 + 17n + 4n2) = 0 Factor a trinomial. 4((-6 + -1n)(7 + -4n)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-6 + -1n)' equal to zero and attempt to solve: Simplifying -6 + -1n = 0 Solving -6 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1n = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1n = 0 + 6 -1n = 0 + 6 Combine like terms: 0 + 6 = 6 -1n = 6 Divide each side by '-1'. n = -6 Simplifying n = -6Subproblem 2
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 = 1.75Solution
n = {-6, 1.75}
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