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Simplifying 10n2 + -6n + -24 = -8 Reorder the terms: -24 + -6n + 10n2 = -8 Solving -24 + -6n + 10n2 = -8 Solving for variable 'n'. Reorder the terms: -24 + 8 + -6n + 10n2 = -8 + 8 Combine like terms: -24 + 8 = -16 -16 + -6n + 10n2 = -8 + 8 Combine like terms: -8 + 8 = 0 -16 + -6n + 10n2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-8 + -3n + 5n2) = 0 Factor a trinomial. 2((-1 + -1n)(8 + -5n)) = 0 Ignore the factor 2.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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