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Simplifying (5 + -1i) * x + 3 = 2 + -4i + 3ix Reorder the terms for easier multiplication: x(5 + -1i) + 3 = 2 + -4i + 3ix (5 * x + -1i * x) + 3 = 2 + -4i + 3ix Reorder the terms: (-1ix + 5x) + 3 = 2 + -4i + 3ix (-1ix + 5x) + 3 = 2 + -4i + 3ix Reorder the terms: 3 + -1ix + 5x = 2 + -4i + 3ix Solving 3 + -1ix + 5x = 2 + -4i + 3ix Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '4i' to each side of the equation. 3 + -1ix + 4i + 5x = 2 + -4i + 4i + 3ix Reorder the terms: 3 + 4i + -1ix + 5x = 2 + -4i + 4i + 3ix Combine like terms: -4i + 4i = 0 3 + 4i + -1ix + 5x = 2 + 0 + 3ix 3 + 4i + -1ix + 5x = 2 + 3ix Add '-3ix' to each side of the equation. 3 + 4i + -1ix + -3ix + 5x = 2 + 3ix + -3ix Combine like terms: -1ix + -3ix = -4ix 3 + 4i + -4ix + 5x = 2 + 3ix + -3ix Combine like terms: 3ix + -3ix = 0 3 + 4i + -4ix + 5x = 2 + 0 3 + 4i + -4ix + 5x = 2 Add '-3' to each side of the equation. 3 + 4i + -4ix + -3 + 5x = 2 + -3 Reorder the terms: 3 + -3 + 4i + -4ix + 5x = 2 + -3 Combine like terms: 3 + -3 = 0 0 + 4i + -4ix + 5x = 2 + -3 4i + -4ix + 5x = 2 + -3 Combine like terms: 2 + -3 = -1 4i + -4ix + 5x = -1 Add '-5x' to each side of the equation. 4i + -4ix + 5x + -5x = -1 + -5x Combine like terms: 5x + -5x = 0 4i + -4ix + 0 = -1 + -5x 4i + -4ix = -1 + -5x Reorder the terms: 1 + 4i + -4ix + 5x = -1 + -5x + 1 + 5x Reorder the terms: 1 + 4i + -4ix + 5x = -1 + 1 + -5x + 5x Combine like terms: -1 + 1 = 0 1 + 4i + -4ix + 5x = 0 + -5x + 5x 1 + 4i + -4ix + 5x = -5x + 5x Combine like terms: -5x + 5x = 0 1 + 4i + -4ix + 5x = 0 The solution to this equation could not be determined.
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