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Simplifying (x + 3)(x + -1 + -1i)(x + -1 + i) = 0 Reorder the terms: (3 + x)(x + -1 + -1i)(x + -1 + i) = 0 Reorder the terms: (3 + x)(-1 + -1i + x)(x + -1 + i) = 0 Reorder the terms: (3 + x)(-1 + -1i + x)(-1 + i + x) = 0 Multiply (3 + x) * (-1 + -1i + x) (3(-1 + -1i + x) + x(-1 + -1i + x))(-1 + i + x) = 0 ((-1 * 3 + -1i * 3 + x * 3) + x(-1 + -1i + x))(-1 + i + x) = 0 ((-3 + -3i + 3x) + x(-1 + -1i + x))(-1 + i + x) = 0 (-3 + -3i + 3x + (-1 * x + -1i * x + x * x))(-1 + i + x) = 0 Reorder the terms: (-3 + -3i + 3x + (-1ix + -1x + x2))(-1 + i + x) = 0 (-3 + -3i + 3x + (-1ix + -1x + x2))(-1 + i + x) = 0 Reorder the terms: (-3 + -3i + -1ix + 3x + -1x + x2)(-1 + i + x) = 0 Combine like terms: 3x + -1x = 2x (-3 + -3i + -1ix + 2x + x2)(-1 + i + x) = 0 Multiply (-3 + -3i + -1ix + 2x + x2) * (-1 + i + x) (-3(-1 + i + x) + -3i * (-1 + i + x) + -1ix * (-1 + i + x) + 2x * (-1 + i + x) + x2(-1 + i + x)) = 0 ((-1 * -3 + i * -3 + x * -3) + -3i * (-1 + i + x) + -1ix * (-1 + i + x) + 2x * (-1 + i + x) + x2(-1 + i + x)) = 0 ((3 + -3i + -3x) + -3i * (-1 + i + x) + -1ix * (-1 + i + x) + 2x * (-1 + i + x) + x2(-1 + i + x)) = 0 (3 + -3i + -3x + (-1 * -3i + i * -3i + x * -3i) + -1ix * (-1 + i + x) + 2x * (-1 + i + x) + x2(-1 + i + x)) = 0 Reorder the terms: (3 + -3i + -3x + (3i + -3ix + -3i2) + -1ix * (-1 + i + x) + 2x * (-1 + i + x) + x2(-1 + i + x)) = 0 (3 + -3i + -3x + (3i + -3ix + -3i2) + -1ix * (-1 + i + x) + 2x * (-1 + i + x) + x2(-1 + i + x)) = 0 (3 + -3i + -3x + 3i + -3ix + -3i2 + (-1 * -1ix + i * -1ix + x * -1ix) + 2x * (-1 + i + x) + x2(-1 + i + x)) = 0 Reorder the terms: (3 + -3i + -3x + 3i + -3ix + -3i2 + (1ix + -1ix2 + -1i2x) + 2x * (-1 + i + x) + x2(-1 + i + x)) = 0 (3 + -3i + -3x + 3i + -3ix + -3i2 + (1ix + -1ix2 + -1i2x) + 2x * (-1 + i + x) + x2(-1 + i + x)) = 0 (3 + -3i + -3x + 3i + -3ix + -3i2 + 1ix + -1ix2 + -1i2x + (-1 * 2x + i * 2x + x * 2x) + x2(-1 + i + x)) = 0 Reorder the terms: (3 + -3i + -3x + 3i + -3ix + -3i2 + 1ix + -1ix2 + -1i2x + (2ix + -2x + 2x2) + x2(-1 + i + x)) = 0 (3 + -3i + -3x + 3i + -3ix + -3i2 + 1ix + -1ix2 + -1i2x + (2ix + -2x + 2x2) + x2(-1 + i + x)) = 0 (3 + -3i + -3x + 3i + -3ix + -3i2 + 1ix + -1ix2 + -1i2x + 2ix + -2x + 2x2 + (-1 * x2 + i * x2 + x * x2)) = 0 Reorder the terms: (3 + -3i + -3x + 3i + -3ix + -3i2 + 1ix + -1ix2 + -1i2x + 2ix + -2x + 2x2 + (ix2 + -1x2 + x3)) = 0 (3 + -3i + -3x + 3i + -3ix + -3i2 + 1ix + -1ix2 + -1i2x + 2ix + -2x + 2x2 + (ix2 + -1x2 + x3)) = 0 Reorder the terms: (3 + -3i + 3i + -3ix + 1ix + 2ix + -1ix2 + ix2 + -3i2 + -1i2x + -3x + -2x + 2x2 + -1x2 + x3) = 0 Combine like terms: -3i + 3i = 0 (3 + 0 + -3ix + 1ix + 2ix + -1ix2 + ix2 + -3i2 + -1i2x + -3x + -2x + 2x2 + -1x2 + x3) = 0 (3 + -3ix + 1ix + 2ix + -1ix2 + ix2 + -3i2 + -1i2x + -3x + -2x + 2x2 + -1x2 + x3) = 0 Combine like terms: -3ix + 1ix = -2ix (3 + -2ix + 2ix + -1ix2 + ix2 + -3i2 + -1i2x + -3x + -2x + 2x2 + -1x2 + x3) = 0 Combine like terms: -2ix + 2ix = 0 (3 + 0 + -1ix2 + ix2 + -3i2 + -1i2x + -3x + -2x + 2x2 + -1x2 + x3) = 0 (3 + -1ix2 + ix2 + -3i2 + -1i2x + -3x + -2x + 2x2 + -1x2 + x3) = 0 Combine like terms: -1ix2 + ix2 = 0 (3 + 0 + -3i2 + -1i2x + -3x + -2x + 2x2 + -1x2 + x3) = 0 (3 + -3i2 + -1i2x + -3x + -2x + 2x2 + -1x2 + x3) = 0 Combine like terms: -3x + -2x = -5x (3 + -3i2 + -1i2x + -5x + 2x2 + -1x2 + x3) = 0 Combine like terms: 2x2 + -1x2 = 1x2 (3 + -3i2 + -1i2x + -5x + 1x2 + x3) = 0 Solving 3 + -3i2 + -1i2x + -5x + 1x2 + x3 = 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 + -3i2 + -1i2x + -5x + 1x2 + -3 + x3 = 0 + -3 Reorder the terms: 3 + -3 + -3i2 + -1i2x + -5x + 1x2 + x3 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -3i2 + -1i2x + -5x + 1x2 + x3 = 0 + -3 -3i2 + -1i2x + -5x + 1x2 + x3 = 0 + -3 Combine like terms: 0 + -3 = -3 -3i2 + -1i2x + -5x + 1x2 + x3 = -3 Add '5x' to each side of the equation. -3i2 + -1i2x + -5x + 1x2 + 5x + x3 = -3 + 5x Reorder the terms: -3i2 + -1i2x + -5x + 5x + 1x2 + x3 = -3 + 5x Combine like terms: -5x + 5x = 0 -3i2 + -1i2x + 0 + 1x2 + x3 = -3 + 5x -3i2 + -1i2x + 1x2 + x3 = -3 + 5x Add '-1x2' to each side of the equation. -3i2 + -1i2x + 1x2 + -1x2 + x3 = -3 + 5x + -1x2 Combine like terms: 1x2 + -1x2 = 0 -3i2 + -1i2x + 0 + x3 = -3 + 5x + -1x2 -3i2 + -1i2x + x3 = -3 + 5x + -1x2 Add '-1x3' to each side of the equation. -3i2 + -1i2x + x3 + -1x3 = -3 + 5x + -1x2 + -1x3 Combine like terms: x3 + -1x3 = 0 -3i2 + -1i2x + 0 = -3 + 5x + -1x2 + -1x3 -3i2 + -1i2x = -3 + 5x + -1x2 + -1x3 Reorder the terms: 3 + -3i2 + -1i2x + -5x + x2 + x3 = -3 + 5x + -1x2 + -1x3 + 3 + -5x + x2 + x3 Reorder the terms: 3 + -3i2 + -1i2x + -5x + x2 + x3 = -3 + 3 + 5x + -5x + -1x2 + x2 + -1x3 + x3 Combine like terms: -3 + 3 = 0 3 + -3i2 + -1i2x + -5x + x2 + x3 = 0 + 5x + -5x + -1x2 + x2 + -1x3 + x3 3 + -3i2 + -1i2x + -5x + x2 + x3 = 5x + -5x + -1x2 + x2 + -1x3 + x3 Combine like terms: 5x + -5x = 0 3 + -3i2 + -1i2x + -5x + x2 + x3 = 0 + -1x2 + x2 + -1x3 + x3 3 + -3i2 + -1i2x + -5x + x2 + x3 = -1x2 + x2 + -1x3 + x3 Combine like terms: -1x2 + x2 = 0 3 + -3i2 + -1i2x + -5x + x2 + x3 = 0 + -1x3 + x3 3 + -3i2 + -1i2x + -5x + x2 + x3 = -1x3 + x3 Combine like terms: -1x3 + x3 = 0 3 + -3i2 + -1i2x + -5x + x2 + x3 = 0 The solution to this equation could not be determined.
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