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Simplifying -6n2 + -8n = -30 + -7n2 + 3n Reorder the terms: -8n + -6n2 = -30 + -7n2 + 3n Reorder the terms: -8n + -6n2 = -30 + 3n + -7n2 Solving -8n + -6n2 = -30 + 3n + -7n2 Solving for variable 'n'. Reorder the terms: 30 + -8n + -3n + -6n2 + 7n2 = -30 + 3n + -7n2 + 30 + -3n + 7n2 Combine like terms: -8n + -3n = -11n 30 + -11n + -6n2 + 7n2 = -30 + 3n + -7n2 + 30 + -3n + 7n2 Combine like terms: -6n2 + 7n2 = 1n2 30 + -11n + 1n2 = -30 + 3n + -7n2 + 30 + -3n + 7n2 Reorder the terms: 30 + -11n + 1n2 = -30 + 30 + 3n + -3n + -7n2 + 7n2 Combine like terms: -30 + 30 = 0 30 + -11n + 1n2 = 0 + 3n + -3n + -7n2 + 7n2 30 + -11n + 1n2 = 3n + -3n + -7n2 + 7n2 Combine like terms: 3n + -3n = 0 30 + -11n + 1n2 = 0 + -7n2 + 7n2 30 + -11n + 1n2 = -7n2 + 7n2 Combine like terms: -7n2 + 7n2 = 0 30 + -11n + 1n2 = 0 Factor a trinomial. (5 + -1n)(6 + -1n) = 0Subproblem 1
Set the factor '(5 + -1n)' equal to zero and attempt to solve: Simplifying 5 + -1n = 0 Solving 5 + -1n = 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 + -1n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1n = 0 + -5 -1n = 0 + -5 Combine like terms: 0 + -5 = -5 -1n = -5 Divide each side by '-1'. n = 5 Simplifying n = 5Subproblem 2
Set the factor '(6 + -1n)' equal to zero and attempt to solve: Simplifying 6 + -1n = 0 Solving 6 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1n = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1n = 0 + -6 -1n = 0 + -6 Combine like terms: 0 + -6 = -6 -1n = -6 Divide each side by '-1'. n = 6 Simplifying n = 6Solution
n = {5, 6}
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