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Simplifying 5n(-2n + 4) + 2n(n + 3) = 0 Reorder the terms: 5n(4 + -2n) + 2n(n + 3) = 0 (4 * 5n + -2n * 5n) + 2n(n + 3) = 0 (20n + -10n2) + 2n(n + 3) = 0 Reorder the terms: 20n + -10n2 + 2n(3 + n) = 0 20n + -10n2 + (3 * 2n + n * 2n) = 0 20n + -10n2 + (6n + 2n2) = 0 Reorder the terms: 20n + 6n + -10n2 + 2n2 = 0 Combine like terms: 20n + 6n = 26n 26n + -10n2 + 2n2 = 0 Combine like terms: -10n2 + 2n2 = -8n2 26n + -8n2 = 0 Solving 26n + -8n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '2n'. 2n(13 + -4n) = 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 '(13 + -4n)' equal to zero and attempt to solve: Simplifying 13 + -4n = 0 Solving 13 + -4n = 0 Move all terms containing n to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + -4n = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -4n = 0 + -13 -4n = 0 + -13 Combine like terms: 0 + -13 = -13 -4n = -13 Divide each side by '-4'. n = 3.25 Simplifying n = 3.25Solution
n = {0, 3.25}
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