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Simplifying 2n(n + 4) + 18 = n(n + 5) + n(n + -2 + -7) Reorder the terms: 2n(4 + n) + 18 = n(n + 5) + n(n + -2 + -7) (4 * 2n + n * 2n) + 18 = n(n + 5) + n(n + -2 + -7) (8n + 2n2) + 18 = n(n + 5) + n(n + -2 + -7) Reorder the terms: 18 + 8n + 2n2 = n(n + 5) + n(n + -2 + -7) Reorder the terms: 18 + 8n + 2n2 = n(5 + n) + n(n + -2 + -7) 18 + 8n + 2n2 = (5 * n + n * n) + n(n + -2 + -7) 18 + 8n + 2n2 = (5n + n2) + n(n + -2 + -7) Reorder the terms: 18 + 8n + 2n2 = 5n + n2 + n(-2 + -7 + n) Combine like terms: -2 + -7 = -9 18 + 8n + 2n2 = 5n + n2 + n(-9 + n) 18 + 8n + 2n2 = 5n + n2 + (-9 * n + n * n) 18 + 8n + 2n2 = 5n + n2 + (-9n + n2) Reorder the terms: 18 + 8n + 2n2 = 5n + -9n + n2 + n2 Combine like terms: 5n + -9n = -4n 18 + 8n + 2n2 = -4n + n2 + n2 Combine like terms: n2 + n2 = 2n2 18 + 8n + 2n2 = -4n + 2n2 Add '-2n2' to each side of the equation. 18 + 8n + 2n2 + -2n2 = -4n + 2n2 + -2n2 Combine like terms: 2n2 + -2n2 = 0 18 + 8n + 0 = -4n + 2n2 + -2n2 18 + 8n = -4n + 2n2 + -2n2 Combine like terms: 2n2 + -2n2 = 0 18 + 8n = -4n + 0 18 + 8n = -4n Solving 18 + 8n = -4n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '4n' to each side of the equation. 18 + 8n + 4n = -4n + 4n Combine like terms: 8n + 4n = 12n 18 + 12n = -4n + 4n Combine like terms: -4n + 4n = 0 18 + 12n = 0 Add '-18' to each side of the equation. 18 + -18 + 12n = 0 + -18 Combine like terms: 18 + -18 = 0 0 + 12n = 0 + -18 12n = 0 + -18 Combine like terms: 0 + -18 = -18 12n = -18 Divide each side by '12'. n = -1.5 Simplifying n = -1.5
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