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Simplifying 5(3n + -2) * 2n = 960 Reorder the terms: 5(-2 + 3n) * 2n = 960 Reorder the terms for easier multiplication: 5 * 2n(-2 + 3n) = 960 Multiply 5 * 2 10n(-2 + 3n) = 960 (-2 * 10n + 3n * 10n) = 960 (-20n + 30n2) = 960 Solving -20n + 30n2 = 960 Solving for variable 'n'. Reorder the terms: -960 + -20n + 30n2 = 960 + -960 Combine like terms: 960 + -960 = 0 -960 + -20n + 30n2 = 0 Factor out the Greatest Common Factor (GCF), '10'. 10(-96 + -2n + 3n2) = 0 Factor a trinomial. 10((-16 + -3n)(6 + -1n)) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(-16 + -3n)' equal to zero and attempt to solve: Simplifying -16 + -3n = 0 Solving -16 + -3n = 0 Move all terms containing n to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + -3n = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -3n = 0 + 16 -3n = 0 + 16 Combine like terms: 0 + 16 = 16 -3n = 16 Divide each side by '-3'. n = -5.333333333 Simplifying n = -5.333333333Subproblem 2
Set the factor '(6 + -1n)' equal to zero and attempt to solve: Simplifying 6 + -1n = 0 Solving 6 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1n = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1n = 0 + -6 -1n = 0 + -6 Combine like terms: 0 + -6 = -6 -1n = -6 Divide each side by '-1'. n = 6 Simplifying n = 6Solution
n = {-5.333333333, 6}
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