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Simplifying 56n2 + 403n + -282 = -2 + -8n2 + -5n Reorder the terms: -282 + 403n + 56n2 = -2 + -8n2 + -5n Reorder the terms: -282 + 403n + 56n2 = -2 + -5n + -8n2 Solving -282 + 403n + 56n2 = -2 + -5n + -8n2 Solving for variable 'n'. Reorder the terms: -282 + 2 + 403n + 5n + 56n2 + 8n2 = -2 + -5n + -8n2 + 2 + 5n + 8n2 Combine like terms: -282 + 2 = -280 -280 + 403n + 5n + 56n2 + 8n2 = -2 + -5n + -8n2 + 2 + 5n + 8n2 Combine like terms: 403n + 5n = 408n -280 + 408n + 56n2 + 8n2 = -2 + -5n + -8n2 + 2 + 5n + 8n2 Combine like terms: 56n2 + 8n2 = 64n2 -280 + 408n + 64n2 = -2 + -5n + -8n2 + 2 + 5n + 8n2 Reorder the terms: -280 + 408n + 64n2 = -2 + 2 + -5n + 5n + -8n2 + 8n2 Combine like terms: -2 + 2 = 0 -280 + 408n + 64n2 = 0 + -5n + 5n + -8n2 + 8n2 -280 + 408n + 64n2 = -5n + 5n + -8n2 + 8n2 Combine like terms: -5n + 5n = 0 -280 + 408n + 64n2 = 0 + -8n2 + 8n2 -280 + 408n + 64n2 = -8n2 + 8n2 Combine like terms: -8n2 + 8n2 = 0 -280 + 408n + 64n2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(-35 + 51n + 8n2) = 0 Factor a trinomial. 8((-7 + -1n)(5 + -8n)) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-7 + -1n)' equal to zero and attempt to solve: Simplifying -7 + -1n = 0 Solving -7 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -1n = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1n = 0 + 7 -1n = 0 + 7 Combine like terms: 0 + 7 = 7 -1n = 7 Divide each side by '-1'. n = -7 Simplifying n = -7Subproblem 2
Set the factor '(5 + -8n)' equal to zero and attempt to solve: Simplifying 5 + -8n = 0 Solving 5 + -8n = 0 Move all terms containing n to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -8n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -8n = 0 + -5 -8n = 0 + -5 Combine like terms: 0 + -5 = -5 -8n = -5 Divide each side by '-8'. n = 0.625 Simplifying n = 0.625Solution
n = {-7, 0.625}
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