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Simplifying 6(6i + 14) = 3(i + 6) Reorder the terms: 6(14 + 6i) = 3(i + 6) (14 * 6 + 6i * 6) = 3(i + 6) (84 + 36i) = 3(i + 6) Reorder the terms: 84 + 36i = 3(6 + i) 84 + 36i = (6 * 3 + i * 3) 84 + 36i = (18 + 3i) Solving 84 + 36i = 18 + 3i Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-3i' to each side of the equation. 84 + 36i + -3i = 18 + 3i + -3i Combine like terms: 36i + -3i = 33i 84 + 33i = 18 + 3i + -3i Combine like terms: 3i + -3i = 0 84 + 33i = 18 + 0 84 + 33i = 18 Add '-84' to each side of the equation. 84 + -84 + 33i = 18 + -84 Combine like terms: 84 + -84 = 0 0 + 33i = 18 + -84 33i = 18 + -84 Combine like terms: 18 + -84 = -66 33i = -66 Divide each side by '33'. i = -2 Simplifying i = -2
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