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Simplifying -59 = -3n2 + 8n + -8 Reorder the terms: -59 = -8 + 8n + -3n2 Solving -59 = -8 + 8n + -3n2 Solving for variable 'n'. Combine like terms: -59 + 8 = -51 -51 + -8n + 3n2 = -8 + 8n + -3n2 + 8 + -8n + 3n2 Reorder the terms: -51 + -8n + 3n2 = -8 + 8 + 8n + -8n + -3n2 + 3n2 Combine like terms: -8 + 8 = 0 -51 + -8n + 3n2 = 0 + 8n + -8n + -3n2 + 3n2 -51 + -8n + 3n2 = 8n + -8n + -3n2 + 3n2 Combine like terms: 8n + -8n = 0 -51 + -8n + 3n2 = 0 + -3n2 + 3n2 -51 + -8n + 3n2 = -3n2 + 3n2 Combine like terms: -3n2 + 3n2 = 0 -51 + -8n + 3n2 = 0 Factor a trinomial. (-3 + -1n)(17 + -3n) = 0Subproblem 1
Set the factor '(-3 + -1n)' equal to zero and attempt to solve: Simplifying -3 + -1n = 0 Solving -3 + -1n = 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 + -1n = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1n = 0 + 3 -1n = 0 + 3 Combine like terms: 0 + 3 = 3 -1n = 3 Divide each side by '-1'. n = -3 Simplifying n = -3Subproblem 2
Set the factor '(17 + -3n)' equal to zero and attempt to solve: Simplifying 17 + -3n = 0 Solving 17 + -3n = 0 Move all terms containing n to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + -3n = 0 + -17 Combine like terms: 17 + -17 = 0 0 + -3n = 0 + -17 -3n = 0 + -17 Combine like terms: 0 + -17 = -17 -3n = -17 Divide each side by '-3'. n = 5.666666667 Simplifying n = 5.666666667Solution
n = {-3, 5.666666667}
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