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Simplifying 84n2 + -8n = 4n2 + 192 Reorder the terms: -8n + 84n2 = 4n2 + 192 Reorder the terms: -8n + 84n2 = 192 + 4n2 Solving -8n + 84n2 = 192 + 4n2 Solving for variable 'n'. Reorder the terms: -192 + -8n + 84n2 + -4n2 = 192 + 4n2 + -192 + -4n2 Combine like terms: 84n2 + -4n2 = 80n2 -192 + -8n + 80n2 = 192 + 4n2 + -192 + -4n2 Reorder the terms: -192 + -8n + 80n2 = 192 + -192 + 4n2 + -4n2 Combine like terms: 192 + -192 = 0 -192 + -8n + 80n2 = 0 + 4n2 + -4n2 -192 + -8n + 80n2 = 4n2 + -4n2 Combine like terms: 4n2 + -4n2 = 0 -192 + -8n + 80n2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(-24 + -1n + 10n2) = 0 Factor a trinomial. 8((-3 + -2n)(8 + -5n)) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-3 + -2n)' equal to zero and attempt to solve: Simplifying -3 + -2n = 0 Solving -3 + -2n = 0 Move all terms containing n to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -2n = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2n = 0 + 3 -2n = 0 + 3 Combine like terms: 0 + 3 = 3 -2n = 3 Divide each side by '-2'. n = -1.5 Simplifying n = -1.5Subproblem 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 = {-1.5, 1.6}
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