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Simplifying 2n(3n + 4) + -19 = n(6n + -2) + 31 Reorder the terms: 2n(4 + 3n) + -19 = n(6n + -2) + 31 (4 * 2n + 3n * 2n) + -19 = n(6n + -2) + 31 (8n + 6n2) + -19 = n(6n + -2) + 31 Reorder the terms: -19 + 8n + 6n2 = n(6n + -2) + 31 Reorder the terms: -19 + 8n + 6n2 = n(-2 + 6n) + 31 -19 + 8n + 6n2 = (-2 * n + 6n * n) + 31 -19 + 8n + 6n2 = (-2n + 6n2) + 31 Reorder the terms: -19 + 8n + 6n2 = 31 + -2n + 6n2 Add '-6n2' to each side of the equation. -19 + 8n + 6n2 + -6n2 = 31 + -2n + 6n2 + -6n2 Combine like terms: 6n2 + -6n2 = 0 -19 + 8n + 0 = 31 + -2n + 6n2 + -6n2 -19 + 8n = 31 + -2n + 6n2 + -6n2 Combine like terms: 6n2 + -6n2 = 0 -19 + 8n = 31 + -2n + 0 -19 + 8n = 31 + -2n Solving -19 + 8n = 31 + -2n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '2n' to each side of the equation. -19 + 8n + 2n = 31 + -2n + 2n Combine like terms: 8n + 2n = 10n -19 + 10n = 31 + -2n + 2n Combine like terms: -2n + 2n = 0 -19 + 10n = 31 + 0 -19 + 10n = 31 Add '19' to each side of the equation. -19 + 19 + 10n = 31 + 19 Combine like terms: -19 + 19 = 0 0 + 10n = 31 + 19 10n = 31 + 19 Combine like terms: 31 + 19 = 50 10n = 50 Divide each side by '10'. n = 5 Simplifying n = 5
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