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Simplifying (5n + 1)(5n + 1) + 2(5n + 1) + -3 = 0 Reorder the terms: (1 + 5n)(5n + 1) + 2(5n + 1) + -3 = 0 Reorder the terms: (1 + 5n)(1 + 5n) + 2(5n + 1) + -3 = 0 Multiply (1 + 5n) * (1 + 5n) (1(1 + 5n) + 5n * (1 + 5n)) + 2(5n + 1) + -3 = 0 ((1 * 1 + 5n * 1) + 5n * (1 + 5n)) + 2(5n + 1) + -3 = 0 ((1 + 5n) + 5n * (1 + 5n)) + 2(5n + 1) + -3 = 0 (1 + 5n + (1 * 5n + 5n * 5n)) + 2(5n + 1) + -3 = 0 (1 + 5n + (5n + 25n2)) + 2(5n + 1) + -3 = 0 Combine like terms: 5n + 5n = 10n (1 + 10n + 25n2) + 2(5n + 1) + -3 = 0 Reorder the terms: 1 + 10n + 25n2 + 2(1 + 5n) + -3 = 0 1 + 10n + 25n2 + (1 * 2 + 5n * 2) + -3 = 0 1 + 10n + 25n2 + (2 + 10n) + -3 = 0 Reorder the terms: 1 + 2 + -3 + 10n + 10n + 25n2 = 0 Combine like terms: 1 + 2 = 3 3 + -3 + 10n + 10n + 25n2 = 0 Combine like terms: 3 + -3 = 0 0 + 10n + 10n + 25n2 = 0 10n + 10n + 25n2 = 0 Combine like terms: 10n + 10n = 20n 20n + 25n2 = 0 Solving 20n + 25n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '5n'. 5n(4 + 5n) = 0 Ignore the factor 5.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 + 5n)' equal to zero and attempt to solve: Simplifying 4 + 5n = 0 Solving 4 + 5n = 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 + 5n = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 5n = 0 + -4 5n = 0 + -4 Combine like terms: 0 + -4 = -4 5n = -4 Divide each side by '5'. n = -0.8 Simplifying n = -0.8Solution
n = {0, -0.8}
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