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Simplifying -3n(1 + -2n) + 2n(5n + -3) = 0 (1 * -3n + -2n * -3n) + 2n(5n + -3) = 0 (-3n + 6n2) + 2n(5n + -3) = 0 Reorder the terms: -3n + 6n2 + 2n(-3 + 5n) = 0 -3n + 6n2 + (-3 * 2n + 5n * 2n) = 0 -3n + 6n2 + (-6n + 10n2) = 0 Reorder the terms: -3n + -6n + 6n2 + 10n2 = 0 Combine like terms: -3n + -6n = -9n -9n + 6n2 + 10n2 = 0 Combine like terms: 6n2 + 10n2 = 16n2 -9n + 16n2 = 0 Solving -9n + 16n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), 'n'. n(-9 + 16n) = 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 '(-9 + 16n)' equal to zero and attempt to solve: Simplifying -9 + 16n = 0 Solving -9 + 16n = 0 Move all terms containing n to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + 16n = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 16n = 0 + 9 16n = 0 + 9 Combine like terms: 0 + 9 = 9 16n = 9 Divide each side by '16'. n = 0.5625 Simplifying n = 0.5625Solution
n = {0, 0.5625}
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