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Simplifying (3x + 4i) + (2 + -3i) + -1(5 + -6i) = 0 Reorder the terms: (4i + 3x) + (2 + -3i) + -1(5 + -6i) = 0 Remove parenthesis around (4i + 3x) 4i + 3x + (2 + -3i) + -1(5 + -6i) = 0 Remove parenthesis around (2 + -3i) 4i + 3x + 2 + -3i + -1(5 + -6i) = 0 4i + 3x + 2 + -3i + (5 * -1 + -6i * -1) = 0 4i + 3x + 2 + -3i + (-5 + 6i) = 0 Reorder the terms: 2 + -5 + 4i + -3i + 6i + 3x = 0 Combine like terms: 2 + -5 = -3 -3 + 4i + -3i + 6i + 3x = 0 Combine like terms: 4i + -3i = 1i -3 + 1i + 6i + 3x = 0 Combine like terms: 1i + 6i = 7i -3 + 7i + 3x = 0 Solving -3 + 7i + 3x = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 7i + 3 + 3x = 0 + 3 Reorder the terms: -3 + 3 + 7i + 3x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 7i + 3x = 0 + 3 7i + 3x = 0 + 3 Combine like terms: 0 + 3 = 3 7i + 3x = 3 Add '-3x' to each side of the equation. 7i + 3x + -3x = 3 + -3x Combine like terms: 3x + -3x = 0 7i + 0 = 3 + -3x 7i = 3 + -3x Divide each side by '7'. i = 0.4285714286 + -0.4285714286x Simplifying i = 0.4285714286 + -0.4285714286x
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