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Simplifying 5n(1 + 3n) + 7n = 0 (1 * 5n + 3n * 5n) + 7n = 0 (5n + 15n2) + 7n = 0 Reorder the terms: 5n + 7n + 15n2 = 0 Combine like terms: 5n + 7n = 12n 12n + 15n2 = 0 Solving 12n + 15n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '3n'. 3n(4 + 5n) = 0 Ignore the factor 3.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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