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Simplifying -4n(-2n + -3) + -2n(1 + 2n) = 0 Reorder the terms: -4n(-3 + -2n) + -2n(1 + 2n) = 0 (-3 * -4n + -2n * -4n) + -2n(1 + 2n) = 0 (12n + 8n2) + -2n(1 + 2n) = 0 12n + 8n2 + (1 * -2n + 2n * -2n) = 0 12n + 8n2 + (-2n + -4n2) = 0 Reorder the terms: 12n + -2n + 8n2 + -4n2 = 0 Combine like terms: 12n + -2n = 10n 10n + 8n2 + -4n2 = 0 Combine like terms: 8n2 + -4n2 = 4n2 10n + 4n2 = 0 Solving 10n + 4n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '2n'. 2n(5 + 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 '(5 + 2n)' equal to zero and attempt to solve: Simplifying 5 + 2n = 0 Solving 5 + 2n = 0 Move all terms containing n to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 2n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2n = 0 + -5 2n = 0 + -5 Combine like terms: 0 + -5 = -5 2n = -5 Divide each side by '2'. n = -2.5 Simplifying n = -2.5Solution
n = {0, -2.5}
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