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Simplifying 7n2 + 10n + -46 = 6n2 + 2 + 8n Reorder the terms: -46 + 10n + 7n2 = 6n2 + 2 + 8n Reorder the terms: -46 + 10n + 7n2 = 2 + 8n + 6n2 Solving -46 + 10n + 7n2 = 2 + 8n + 6n2 Solving for variable 'n'. Reorder the terms: -46 + -2 + 10n + -8n + 7n2 + -6n2 = 2 + 8n + 6n2 + -2 + -8n + -6n2 Combine like terms: -46 + -2 = -48 -48 + 10n + -8n + 7n2 + -6n2 = 2 + 8n + 6n2 + -2 + -8n + -6n2 Combine like terms: 10n + -8n = 2n -48 + 2n + 7n2 + -6n2 = 2 + 8n + 6n2 + -2 + -8n + -6n2 Combine like terms: 7n2 + -6n2 = 1n2 -48 + 2n + 1n2 = 2 + 8n + 6n2 + -2 + -8n + -6n2 Reorder the terms: -48 + 2n + 1n2 = 2 + -2 + 8n + -8n + 6n2 + -6n2 Combine like terms: 2 + -2 = 0 -48 + 2n + 1n2 = 0 + 8n + -8n + 6n2 + -6n2 -48 + 2n + 1n2 = 8n + -8n + 6n2 + -6n2 Combine like terms: 8n + -8n = 0 -48 + 2n + 1n2 = 0 + 6n2 + -6n2 -48 + 2n + 1n2 = 6n2 + -6n2 Combine like terms: 6n2 + -6n2 = 0 -48 + 2n + 1n2 = 0 Factor a trinomial. (-8 + -1n)(6 + -1n) = 0Subproblem 1
Set the factor '(-8 + -1n)' equal to zero and attempt to solve: Simplifying -8 + -1n = 0 Solving -8 + -1n = 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 + -1n = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -1n = 0 + 8 -1n = 0 + 8 Combine like terms: 0 + 8 = 8 -1n = 8 Divide each side by '-1'. n = -8 Simplifying n = -8Subproblem 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 = {-8, 6}
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