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Simplifying An = 5n(n + 2) Reorder the terms: nA = 5n(2 + n) nA = (2 * 5n + n * 5n) nA = (10n + 5n2) Solving nA = 10n + 5n2 Solving for variable 'n'. Reorder the terms: -10n + nA + -5n2 = 10n + 5n2 + -10n + -5n2 Reorder the terms: -10n + nA + -5n2 = 10n + -10n + 5n2 + -5n2 Combine like terms: 10n + -10n = 0 -10n + nA + -5n2 = 0 + 5n2 + -5n2 -10n + nA + -5n2 = 5n2 + -5n2 Combine like terms: 5n2 + -5n2 = 0 -10n + nA + -5n2 = 0 Factor out the Greatest Common Factor (GCF), 'n'. n(-10 + A + -5n) = 0Subproblem 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 '(-10 + A + -5n)' equal to zero and attempt to solve: Simplifying -10 + A + -5n = 0 Solving -10 + A + -5n = 0 Move all terms containing n to the left, all other terms to the right. Add '10' to each side of the equation. -10 + A + 10 + -5n = 0 + 10 Reorder the terms: -10 + 10 + A + -5n = 0 + 10 Combine like terms: -10 + 10 = 0 0 + A + -5n = 0 + 10 A + -5n = 0 + 10 Combine like terms: 0 + 10 = 10 A + -5n = 10 Add '-1A' to each side of the equation. A + -1A + -5n = 10 + -1A Combine like terms: A + -1A = 0 0 + -5n = 10 + -1A -5n = 10 + -1A Divide each side by '-5'. n = -2 + 0.2A Simplifying n = -2 + 0.2ASolution
n = {0, -2 + 0.2A}
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