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Simplifying -2n(-4n + -2) + 2n(6 + -6n) = 0 Reorder the terms: -2n(-2 + -4n) + 2n(6 + -6n) = 0 (-2 * -2n + -4n * -2n) + 2n(6 + -6n) = 0 (4n + 8n2) + 2n(6 + -6n) = 0 4n + 8n2 + (6 * 2n + -6n * 2n) = 0 4n + 8n2 + (12n + -12n2) = 0 Reorder the terms: 4n + 12n + 8n2 + -12n2 = 0 Combine like terms: 4n + 12n = 16n 16n + 8n2 + -12n2 = 0 Combine like terms: 8n2 + -12n2 = -4n2 16n + -4n2 = 0 Solving 16n + -4n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '4n'. 4n(4 + -1n) = 0 Ignore the factor 4.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 '(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 = {0, 4}
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