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Simplifying 9n(n + 2) + -5n(n + 3) = 0 Reorder the terms: 9n(2 + n) + -5n(n + 3) = 0 (2 * 9n + n * 9n) + -5n(n + 3) = 0 (18n + 9n2) + -5n(n + 3) = 0 Reorder the terms: 18n + 9n2 + -5n(3 + n) = 0 18n + 9n2 + (3 * -5n + n * -5n) = 0 18n + 9n2 + (-15n + -5n2) = 0 Reorder the terms: 18n + -15n + 9n2 + -5n2 = 0 Combine like terms: 18n + -15n = 3n 3n + 9n2 + -5n2 = 0 Combine like terms: 9n2 + -5n2 = 4n2 3n + 4n2 = 0 Solving 3n + 4n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), 'n'. n(3 + 4n) = 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 '(3 + 4n)' equal to zero and attempt to solve: Simplifying 3 + 4n = 0 Solving 3 + 4n = 0 Move all terms containing n to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 4n = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 4n = 0 + -3 4n = 0 + -3 Combine like terms: 0 + -3 = -3 4n = -3 Divide each side by '4'. n = -0.75 Simplifying n = -0.75Solution
n = {0, -0.75}
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