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Simplifying 12n2 + -56n + 64 = 0 Reorder the terms: 64 + -56n + 12n2 = 0 Solving 64 + -56n + 12n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '4'. 4(16 + -14n + 3n2) = 0 Factor a trinomial. 4((2 + -1n)(8 + -3n)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(2 + -1n)' equal to zero and attempt to solve: Simplifying 2 + -1n = 0 Solving 2 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1n = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1n = 0 + -2 -1n = 0 + -2 Combine like terms: 0 + -2 = -2 -1n = -2 Divide each side by '-1'. n = 2 Simplifying n = 2Subproblem 2
Set the factor '(8 + -3n)' equal to zero and attempt to solve: Simplifying 8 + -3n = 0 Solving 8 + -3n = 0 Move all terms containing n to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -3n = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -3n = 0 + -8 -3n = 0 + -8 Combine like terms: 0 + -8 = -8 -3n = -8 Divide each side by '-3'. n = 2.666666667 Simplifying n = 2.666666667Solution
n = {2, 2.666666667}
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