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Simplifying (1 + 3i) * 2x + 4x + 2ix = (1 + 5i) * x + -6i Reorder the terms for easier multiplication: 2x(1 + 3i) + 4x + 2ix = (1 + 5i) * x + -6i (1 * 2x + 3i * 2x) + 4x + 2ix = (1 + 5i) * x + -6i Reorder the terms: (6ix + 2x) + 4x + 2ix = (1 + 5i) * x + -6i (6ix + 2x) + 4x + 2ix = (1 + 5i) * x + -6i Reorder the terms: 6ix + 2ix + 2x + 4x = (1 + 5i) * x + -6i Combine like terms: 6ix + 2ix = 8ix 8ix + 2x + 4x = (1 + 5i) * x + -6i Combine like terms: 2x + 4x = 6x 8ix + 6x = (1 + 5i) * x + -6i Reorder the terms for easier multiplication: 8ix + 6x = x(1 + 5i) + -6i 8ix + 6x = (1 * x + 5i * x) + -6i Reorder the terms: 8ix + 6x = (5ix + 1x) + -6i 8ix + 6x = (5ix + 1x) + -6i Reorder the terms: 8ix + 6x = -6i + 5ix + 1x Solving 8ix + 6x = -6i + 5ix + 1x Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '6i' to each side of the equation. 8ix + 6i + 6x = -6i + 5ix + 6i + 1x Reorder the terms: 6i + 8ix + 6x = -6i + 5ix + 6i + 1x Reorder the terms: 6i + 8ix + 6x = -6i + 6i + 5ix + 1x Combine like terms: -6i + 6i = 0 6i + 8ix + 6x = 0 + 5ix + 1x 6i + 8ix + 6x = 5ix + 1x Add '-5ix' to each side of the equation. 6i + 8ix + -5ix + 6x = 5ix + -5ix + 1x Combine like terms: 8ix + -5ix = 3ix 6i + 3ix + 6x = 5ix + -5ix + 1x Combine like terms: 5ix + -5ix = 0 6i + 3ix + 6x = 0 + 1x 6i + 3ix + 6x = 1x Add '-6x' to each side of the equation. 6i + 3ix + 6x + -6x = 1x + -6x Combine like terms: 6x + -6x = 0 6i + 3ix + 0 = 1x + -6x 6i + 3ix = 1x + -6x Combine like terms: 1x + -6x = -5x 6i + 3ix = -5x Combine like terms: -5x + 5x = 0 6i + 3ix + 5x = 0 The solution to this equation could not be determined.
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