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Simplifying 2n = 4n(n + -8) Reorder the terms: 2n = 4n(-8 + n) 2n = (-8 * 4n + n * 4n) 2n = (-32n + 4n2) Solving 2n = -32n + 4n2 Solving for variable 'n'. Combine like terms: 2n + 32n = 34n 34n + -4n2 = -32n + 4n2 + 32n + -4n2 Reorder the terms: 34n + -4n2 = -32n + 32n + 4n2 + -4n2 Combine like terms: -32n + 32n = 0 34n + -4n2 = 0 + 4n2 + -4n2 34n + -4n2 = 4n2 + -4n2 Combine like terms: 4n2 + -4n2 = 0 34n + -4n2 = 0 Factor out the Greatest Common Factor (GCF), '2n'. 2n(17 + -2n) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'n' equal to zero and attempt to solve: Simplifying n = 0 Solving n = 0 Move all terms containing n to the left, all other terms to the right. Simplifying n = 0Subproblem 2
Set the factor '(17 + -2n)' equal to zero and attempt to solve: Simplifying 17 + -2n = 0 Solving 17 + -2n = 0 Move all terms containing n to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + -2n = 0 + -17 Combine like terms: 17 + -17 = 0 0 + -2n = 0 + -17 -2n = 0 + -17 Combine like terms: 0 + -17 = -17 -2n = -17 Divide each side by '-2'. n = 8.5 Simplifying n = 8.5Solution
n = {0, 8.5}
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