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Simplifying -3n(5n + 3) = -24 Reorder the terms: -3n(3 + 5n) = -24 (3 * -3n + 5n * -3n) = -24 (-9n + -15n2) = -24 Solving -9n + -15n2 = -24 Solving for variable 'n'. Reorder the terms: 24 + -9n + -15n2 = -24 + 24 Combine like terms: -24 + 24 = 0 24 + -9n + -15n2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(8 + -3n + -5n2) = 0 Factor a trinomial. 3((1 + -1n)(8 + 5n)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(1 + -1n)' equal to zero and attempt to solve: Simplifying 1 + -1n = 0 Solving 1 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1n = 0 + -1 -1n = 0 + -1 Combine like terms: 0 + -1 = -1 -1n = -1 Divide each side by '-1'. n = 1 Simplifying n = 1Subproblem 2
Set the factor '(8 + 5n)' equal to zero and attempt to solve: Simplifying 8 + 5n = 0 Solving 8 + 5n = 0 Move all terms containing n to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + 5n = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 5n = 0 + -8 5n = 0 + -8 Combine like terms: 0 + -8 = -8 5n = -8 Divide each side by '5'. n = -1.6 Simplifying n = -1.6Solution
n = {1, -1.6}
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