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Simplifying (x + 3)(x + -1(-1 + 2i))(x + -1(-1 + -2i)) = 0 Reorder the terms: (3 + x)(x + -1(-1 + 2i))(x + -1(-1 + -2i)) = 0 (3 + x)(x + (-1 * -1 + 2i * -1))(x + -1(-1 + -2i)) = 0 (3 + x)(x + (1 + -2i))(x + -1(-1 + -2i)) = 0 Reorder the terms: (3 + x)(1 + -2i + x)(x + -1(-1 + -2i)) = 0 (3 + x)(1 + -2i + x)(x + (-1 * -1 + -2i * -1)) = 0 (3 + x)(1 + -2i + x)(x + (1 + 2i)) = 0 Reorder the terms: (3 + x)(1 + -2i + x)(1 + 2i + x) = 0 Multiply (3 + x) * (1 + -2i + x) (3(1 + -2i + x) + x(1 + -2i + x))(1 + 2i + x) = 0 ((1 * 3 + -2i * 3 + x * 3) + x(1 + -2i + x))(1 + 2i + x) = 0 ((3 + -6i + 3x) + x(1 + -2i + x))(1 + 2i + x) = 0 (3 + -6i + 3x + (1 * x + -2i * x + x * x))(1 + 2i + x) = 0 Reorder the terms: (3 + -6i + 3x + (-2ix + 1x + x2))(1 + 2i + x) = 0 (3 + -6i + 3x + (-2ix + 1x + x2))(1 + 2i + x) = 0 Reorder the terms: (3 + -6i + -2ix + 3x + 1x + x2)(1 + 2i + x) = 0 Combine like terms: 3x + 1x = 4x (3 + -6i + -2ix + 4x + x2)(1 + 2i + x) = 0 Multiply (3 + -6i + -2ix + 4x + x2) * (1 + 2i + x) (3(1 + 2i + x) + -6i * (1 + 2i + x) + -2ix * (1 + 2i + x) + 4x * (1 + 2i + x) + x2(1 + 2i + x)) = 0 ((1 * 3 + 2i * 3 + x * 3) + -6i * (1 + 2i + x) + -2ix * (1 + 2i + x) + 4x * (1 + 2i + x) + x2(1 + 2i + x)) = 0 ((3 + 6i + 3x) + -6i * (1 + 2i + x) + -2ix * (1 + 2i + x) + 4x * (1 + 2i + x) + x2(1 + 2i + x)) = 0 (3 + 6i + 3x + (1 * -6i + 2i * -6i + x * -6i) + -2ix * (1 + 2i + x) + 4x * (1 + 2i + x) + x2(1 + 2i + x)) = 0 Reorder the terms: (3 + 6i + 3x + (-6i + -6ix + -12i2) + -2ix * (1 + 2i + x) + 4x * (1 + 2i + x) + x2(1 + 2i + x)) = 0 (3 + 6i + 3x + (-6i + -6ix + -12i2) + -2ix * (1 + 2i + x) + 4x * (1 + 2i + x) + x2(1 + 2i + x)) = 0 (3 + 6i + 3x + -6i + -6ix + -12i2 + (1 * -2ix + 2i * -2ix + x * -2ix) + 4x * (1 + 2i + x) + x2(1 + 2i + x)) = 0 Reorder the terms: (3 + 6i + 3x + -6i + -6ix + -12i2 + (-2ix + -2ix2 + -4i2x) + 4x * (1 + 2i + x) + x2(1 + 2i + x)) = 0 (3 + 6i + 3x + -6i + -6ix + -12i2 + (-2ix + -2ix2 + -4i2x) + 4x * (1 + 2i + x) + x2(1 + 2i + x)) = 0 (3 + 6i + 3x + -6i + -6ix + -12i2 + -2ix + -2ix2 + -4i2x + (1 * 4x + 2i * 4x + x * 4x) + x2(1 + 2i + x)) = 0 Reorder the terms: (3 + 6i + 3x + -6i + -6ix + -12i2 + -2ix + -2ix2 + -4i2x + (8ix + 4x + 4x2) + x2(1 + 2i + x)) = 0 (3 + 6i + 3x + -6i + -6ix + -12i2 + -2ix + -2ix2 + -4i2x + (8ix + 4x + 4x2) + x2(1 + 2i + x)) = 0 (3 + 6i + 3x + -6i + -6ix + -12i2 + -2ix + -2ix2 + -4i2x + 8ix + 4x + 4x2 + (1 * x2 + 2i * x2 + x * x2)) = 0 Reorder the terms: (3 + 6i + 3x + -6i + -6ix + -12i2 + -2ix + -2ix2 + -4i2x + 8ix + 4x + 4x2 + (2ix2 + 1x2 + x3)) = 0 (3 + 6i + 3x + -6i + -6ix + -12i2 + -2ix + -2ix2 + -4i2x + 8ix + 4x + 4x2 + (2ix2 + 1x2 + x3)) = 0 Reorder the terms: (3 + 6i + -6i + -6ix + -2ix + 8ix + -2ix2 + 2ix2 + -12i2 + -4i2x + 3x + 4x + 4x2 + 1x2 + x3) = 0 Combine like terms: 6i + -6i = 0 (3 + 0 + -6ix + -2ix + 8ix + -2ix2 + 2ix2 + -12i2 + -4i2x + 3x + 4x + 4x2 + 1x2 + x3) = 0 (3 + -6ix + -2ix + 8ix + -2ix2 + 2ix2 + -12i2 + -4i2x + 3x + 4x + 4x2 + 1x2 + x3) = 0 Combine like terms: -6ix + -2ix = -8ix (3 + -8ix + 8ix + -2ix2 + 2ix2 + -12i2 + -4i2x + 3x + 4x + 4x2 + 1x2 + x3) = 0 Combine like terms: -8ix + 8ix = 0 (3 + 0 + -2ix2 + 2ix2 + -12i2 + -4i2x + 3x + 4x + 4x2 + 1x2 + x3) = 0 (3 + -2ix2 + 2ix2 + -12i2 + -4i2x + 3x + 4x + 4x2 + 1x2 + x3) = 0 Combine like terms: -2ix2 + 2ix2 = 0 (3 + 0 + -12i2 + -4i2x + 3x + 4x + 4x2 + 1x2 + x3) = 0 (3 + -12i2 + -4i2x + 3x + 4x + 4x2 + 1x2 + x3) = 0 Combine like terms: 3x + 4x = 7x (3 + -12i2 + -4i2x + 7x + 4x2 + 1x2 + x3) = 0 Combine like terms: 4x2 + 1x2 = 5x2 (3 + -12i2 + -4i2x + 7x + 5x2 + x3) = 0 Solving 3 + -12i2 + -4i2x + 7x + 5x2 + 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 + -12i2 + -4i2x + 7x + 5x2 + -3 + x3 = 0 + -3 Reorder the terms: 3 + -3 + -12i2 + -4i2x + 7x + 5x2 + x3 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -12i2 + -4i2x + 7x + 5x2 + x3 = 0 + -3 -12i2 + -4i2x + 7x + 5x2 + x3 = 0 + -3 Combine like terms: 0 + -3 = -3 -12i2 + -4i2x + 7x + 5x2 + x3 = -3 Add '-7x' to each side of the equation. -12i2 + -4i2x + 7x + 5x2 + -7x + x3 = -3 + -7x Reorder the terms: -12i2 + -4i2x + 7x + -7x + 5x2 + x3 = -3 + -7x Combine like terms: 7x + -7x = 0 -12i2 + -4i2x + 0 + 5x2 + x3 = -3 + -7x -12i2 + -4i2x + 5x2 + x3 = -3 + -7x Add '-5x2' to each side of the equation. -12i2 + -4i2x + 5x2 + -5x2 + x3 = -3 + -7x + -5x2 Combine like terms: 5x2 + -5x2 = 0 -12i2 + -4i2x + 0 + x3 = -3 + -7x + -5x2 -12i2 + -4i2x + x3 = -3 + -7x + -5x2 Add '-1x3' to each side of the equation. -12i2 + -4i2x + x3 + -1x3 = -3 + -7x + -5x2 + -1x3 Combine like terms: x3 + -1x3 = 0 -12i2 + -4i2x + 0 = -3 + -7x + -5x2 + -1x3 -12i2 + -4i2x = -3 + -7x + -5x2 + -1x3 Reorder the terms: 3 + -12i2 + -4i2x + 7x + 5x2 + x3 = -3 + -7x + -5x2 + -1x3 + 3 + 7x + 5x2 + x3 Reorder the terms: 3 + -12i2 + -4i2x + 7x + 5x2 + x3 = -3 + 3 + -7x + 7x + -5x2 + 5x2 + -1x3 + x3 Combine like terms: -3 + 3 = 0 3 + -12i2 + -4i2x + 7x + 5x2 + x3 = 0 + -7x + 7x + -5x2 + 5x2 + -1x3 + x3 3 + -12i2 + -4i2x + 7x + 5x2 + x3 = -7x + 7x + -5x2 + 5x2 + -1x3 + x3 Combine like terms: -7x + 7x = 0 3 + -12i2 + -4i2x + 7x + 5x2 + x3 = 0 + -5x2 + 5x2 + -1x3 + x3 3 + -12i2 + -4i2x + 7x + 5x2 + x3 = -5x2 + 5x2 + -1x3 + x3 Combine like terms: -5x2 + 5x2 = 0 3 + -12i2 + -4i2x + 7x + 5x2 + x3 = 0 + -1x3 + x3 3 + -12i2 + -4i2x + 7x + 5x2 + x3 = -1x3 + x3 Combine like terms: -1x3 + x3 = 0 3 + -12i2 + -4i2x + 7x + 5x2 + x3 = 0 The solution to this equation could not be determined.
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