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Simplifying 5n2 + 6n + -16 = -5n2 Reorder the terms: -16 + 6n + 5n2 = -5n2 Solving -16 + 6n + 5n2 = -5n2 Solving for variable 'n'. Combine like terms: 5n2 + 5n2 = 10n2 -16 + 6n + 10n2 = -5n2 + 5n2 Combine like terms: -5n2 + 5n2 = 0 -16 + 6n + 10n2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-8 + 3n + 5n2) = 0 Factor a trinomial. 2((-8 + -5n)(1 + -1n)) = 0 Ignore the factor 2.Subproblem 1
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 = -1.6Subproblem 2
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 = 1Solution
n = {-1.6, 1}
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