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Simplifying 6(3i + -5) = 2(5i + 5) Reorder the terms: 6(-5 + 3i) = 2(5i + 5) (-5 * 6 + 3i * 6) = 2(5i + 5) (-30 + 18i) = 2(5i + 5) Reorder the terms: -30 + 18i = 2(5 + 5i) -30 + 18i = (5 * 2 + 5i * 2) -30 + 18i = (10 + 10i) Solving -30 + 18i = 10 + 10i Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-10i' to each side of the equation. -30 + 18i + -10i = 10 + 10i + -10i Combine like terms: 18i + -10i = 8i -30 + 8i = 10 + 10i + -10i Combine like terms: 10i + -10i = 0 -30 + 8i = 10 + 0 -30 + 8i = 10 Add '30' to each side of the equation. -30 + 30 + 8i = 10 + 30 Combine like terms: -30 + 30 = 0 0 + 8i = 10 + 30 8i = 10 + 30 Combine like terms: 10 + 30 = 40 8i = 40 Divide each side by '8'. i = 5 Simplifying i = 5
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