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Simplifying -3n(8 + 2n) + n(1 + -3n) = 0 (8 * -3n + 2n * -3n) + n(1 + -3n) = 0 (-24n + -6n2) + n(1 + -3n) = 0 -24n + -6n2 + (1 * n + -3n * n) = 0 -24n + -6n2 + (1n + -3n2) = 0 Reorder the terms: -24n + 1n + -6n2 + -3n2 = 0 Combine like terms: -24n + 1n = -23n -23n + -6n2 + -3n2 = 0 Combine like terms: -6n2 + -3n2 = -9n2 -23n + -9n2 = 0 Solving -23n + -9n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '-1n'. -1n(23 + 9n) = 0 Ignore the factor -1.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 '(23 + 9n)' equal to zero and attempt to solve: Simplifying 23 + 9n = 0 Solving 23 + 9n = 0 Move all terms containing n to the left, all other terms to the right. Add '-23' to each side of the equation. 23 + -23 + 9n = 0 + -23 Combine like terms: 23 + -23 = 0 0 + 9n = 0 + -23 9n = 0 + -23 Combine like terms: 0 + -23 = -23 9n = -23 Divide each side by '9'. n = -2.555555556 Simplifying n = -2.555555556Solution
n = {0, -2.555555556}
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