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Simplifying 2[7 + -7(1 + -1n)] + 7n = 0.34 + 6[6(n + 1) + -3n] 2[7 + (1 * -7 + -1n * -7)] + 7n = 0.34 + 6[6(n + 1) + -3n] 2[7 + (-7 + 7n)] + 7n = 0.34 + 6[6(n + 1) + -3n] Combine like terms: 7 + -7 = 0 2[0 + 7n] + 7n = 0.34 + 6[6(n + 1) + -3n] 2[7n] + 7n = 0.34 + 6[6(n + 1) + -3n] Remove brackets around [7n] 2 * 7n + 7n = 0.34 + 6[6(n + 1) + -3n] Multiply 2 * 7 14n + 7n = 0.34 + 6[6(n + 1) + -3n] Combine like terms: 14n + 7n = 21n 21n = 0.34 + 6[6(n + 1) + -3n] Reorder the terms: 21n = 0.34 + 6[6(1 + n) + -3n] 21n = 0.34 + 6[(1 * 6 + n * 6) + -3n] 21n = 0.34 + 6[(6 + 6n) + -3n] Combine like terms: 6n + -3n = 3n 21n = 0.34 + 6[6 + 3n] 21n = 0.34 + [6 * 6 + 3n * 6] 21n = 0.34 + [36 + 18n] Combine like terms: 0.34 + 36 = 36.34 21n = 36.34 + 18n Solving 21n = 36.34 + 18n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-18n' to each side of the equation. 21n + -18n = 36.34 + 18n + -18n Combine like terms: 21n + -18n = 3n 3n = 36.34 + 18n + -18n Combine like terms: 18n + -18n = 0 3n = 36.34 + 0 3n = 36.34 Divide each side by '3'. n = 12.11333333 Simplifying n = 12.11333333
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