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Simplifying (x + 2)(x + -1(3 + -1i))(x + -1(3 + i)) = 0 Reorder the terms: (2 + x)(x + -1(3 + -1i))(x + -1(3 + i)) = 0 (2 + x)(x + (3 * -1 + -1i * -1))(x + -1(3 + i)) = 0 (2 + x)(x + (-3 + 1i))(x + -1(3 + i)) = 0 Reorder the terms: (2 + x)(-3 + 1i + x)(x + -1(3 + i)) = 0 (2 + x)(-3 + 1i + x)(x + (3 * -1 + i * -1)) = 0 (2 + x)(-3 + 1i + x)(x + (-3 + -1i)) = 0 Reorder the terms: (2 + x)(-3 + 1i + x)(-3 + -1i + x) = 0 Multiply (2 + x) * (-3 + 1i + x) (2(-3 + 1i + x) + x(-3 + 1i + x))(-3 + -1i + x) = 0 ((-3 * 2 + 1i * 2 + x * 2) + x(-3 + 1i + x))(-3 + -1i + x) = 0 ((-6 + 2i + 2x) + x(-3 + 1i + x))(-3 + -1i + x) = 0 (-6 + 2i + 2x + (-3 * x + 1i * x + x * x))(-3 + -1i + x) = 0 Reorder the terms: (-6 + 2i + 2x + (1ix + -3x + x2))(-3 + -1i + x) = 0 (-6 + 2i + 2x + (1ix + -3x + x2))(-3 + -1i + x) = 0 Reorder the terms: (-6 + 2i + 1ix + 2x + -3x + x2)(-3 + -1i + x) = 0 Combine like terms: 2x + -3x = -1x (-6 + 2i + 1ix + -1x + x2)(-3 + -1i + x) = 0 Multiply (-6 + 2i + 1ix + -1x + x2) * (-3 + -1i + x) (-6(-3 + -1i + x) + 2i * (-3 + -1i + x) + 1ix * (-3 + -1i + x) + -1x * (-3 + -1i + x) + x2(-3 + -1i + x)) = 0 ((-3 * -6 + -1i * -6 + x * -6) + 2i * (-3 + -1i + x) + 1ix * (-3 + -1i + x) + -1x * (-3 + -1i + x) + x2(-3 + -1i + x)) = 0 ((18 + 6i + -6x) + 2i * (-3 + -1i + x) + 1ix * (-3 + -1i + x) + -1x * (-3 + -1i + x) + x2(-3 + -1i + x)) = 0 (18 + 6i + -6x + (-3 * 2i + -1i * 2i + x * 2i) + 1ix * (-3 + -1i + x) + -1x * (-3 + -1i + x) + x2(-3 + -1i + x)) = 0 Reorder the terms: (18 + 6i + -6x + (-6i + 2ix + -2i2) + 1ix * (-3 + -1i + x) + -1x * (-3 + -1i + x) + x2(-3 + -1i + x)) = 0 (18 + 6i + -6x + (-6i + 2ix + -2i2) + 1ix * (-3 + -1i + x) + -1x * (-3 + -1i + x) + x2(-3 + -1i + x)) = 0 (18 + 6i + -6x + -6i + 2ix + -2i2 + (-3 * 1ix + -1i * 1ix + x * 1ix) + -1x * (-3 + -1i + x) + x2(-3 + -1i + x)) = 0 Reorder the terms: (18 + 6i + -6x + -6i + 2ix + -2i2 + (-3ix + 1ix2 + -1i2x) + -1x * (-3 + -1i + x) + x2(-3 + -1i + x)) = 0 (18 + 6i + -6x + -6i + 2ix + -2i2 + (-3ix + 1ix2 + -1i2x) + -1x * (-3 + -1i + x) + x2(-3 + -1i + x)) = 0 (18 + 6i + -6x + -6i + 2ix + -2i2 + -3ix + 1ix2 + -1i2x + (-3 * -1x + -1i * -1x + x * -1x) + x2(-3 + -1i + x)) = 0 Reorder the terms: (18 + 6i + -6x + -6i + 2ix + -2i2 + -3ix + 1ix2 + -1i2x + (1ix + 3x + -1x2) + x2(-3 + -1i + x)) = 0 (18 + 6i + -6x + -6i + 2ix + -2i2 + -3ix + 1ix2 + -1i2x + (1ix + 3x + -1x2) + x2(-3 + -1i + x)) = 0 (18 + 6i + -6x + -6i + 2ix + -2i2 + -3ix + 1ix2 + -1i2x + 1ix + 3x + -1x2 + (-3 * x2 + -1i * x2 + x * x2)) = 0 Reorder the terms: (18 + 6i + -6x + -6i + 2ix + -2i2 + -3ix + 1ix2 + -1i2x + 1ix + 3x + -1x2 + (-1ix2 + -3x2 + x3)) = 0 (18 + 6i + -6x + -6i + 2ix + -2i2 + -3ix + 1ix2 + -1i2x + 1ix + 3x + -1x2 + (-1ix2 + -3x2 + x3)) = 0 Reorder the terms: (18 + 6i + -6i + 2ix + -3ix + 1ix + 1ix2 + -1ix2 + -2i2 + -1i2x + -6x + 3x + -1x2 + -3x2 + x3) = 0 Combine like terms: 6i + -6i = 0 (18 + 0 + 2ix + -3ix + 1ix + 1ix2 + -1ix2 + -2i2 + -1i2x + -6x + 3x + -1x2 + -3x2 + x3) = 0 (18 + 2ix + -3ix + 1ix + 1ix2 + -1ix2 + -2i2 + -1i2x + -6x + 3x + -1x2 + -3x2 + x3) = 0 Combine like terms: 2ix + -3ix = -1ix (18 + -1ix + 1ix + 1ix2 + -1ix2 + -2i2 + -1i2x + -6x + 3x + -1x2 + -3x2 + x3) = 0 Combine like terms: -1ix + 1ix = 0 (18 + 0 + 1ix2 + -1ix2 + -2i2 + -1i2x + -6x + 3x + -1x2 + -3x2 + x3) = 0 (18 + 1ix2 + -1ix2 + -2i2 + -1i2x + -6x + 3x + -1x2 + -3x2 + x3) = 0 Combine like terms: 1ix2 + -1ix2 = 0 (18 + 0 + -2i2 + -1i2x + -6x + 3x + -1x2 + -3x2 + x3) = 0 (18 + -2i2 + -1i2x + -6x + 3x + -1x2 + -3x2 + x3) = 0 Combine like terms: -6x + 3x = -3x (18 + -2i2 + -1i2x + -3x + -1x2 + -3x2 + x3) = 0 Combine like terms: -1x2 + -3x2 = -4x2 (18 + -2i2 + -1i2x + -3x + -4x2 + x3) = 0 Solving 18 + -2i2 + -1i2x + -3x + -4x2 + x3 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -2i2 + -1i2x + -3x + -4x2 + -18 + x3 = 0 + -18 Reorder the terms: 18 + -18 + -2i2 + -1i2x + -3x + -4x2 + x3 = 0 + -18 Combine like terms: 18 + -18 = 0 0 + -2i2 + -1i2x + -3x + -4x2 + x3 = 0 + -18 -2i2 + -1i2x + -3x + -4x2 + x3 = 0 + -18 Combine like terms: 0 + -18 = -18 -2i2 + -1i2x + -3x + -4x2 + x3 = -18 Add '3x' to each side of the equation. -2i2 + -1i2x + -3x + -4x2 + 3x + x3 = -18 + 3x Reorder the terms: -2i2 + -1i2x + -3x + 3x + -4x2 + x3 = -18 + 3x Combine like terms: -3x + 3x = 0 -2i2 + -1i2x + 0 + -4x2 + x3 = -18 + 3x -2i2 + -1i2x + -4x2 + x3 = -18 + 3x Add '4x2' to each side of the equation. -2i2 + -1i2x + -4x2 + 4x2 + x3 = -18 + 3x + 4x2 Combine like terms: -4x2 + 4x2 = 0 -2i2 + -1i2x + 0 + x3 = -18 + 3x + 4x2 -2i2 + -1i2x + x3 = -18 + 3x + 4x2 Add '-1x3' to each side of the equation. -2i2 + -1i2x + x3 + -1x3 = -18 + 3x + 4x2 + -1x3 Combine like terms: x3 + -1x3 = 0 -2i2 + -1i2x + 0 = -18 + 3x + 4x2 + -1x3 -2i2 + -1i2x = -18 + 3x + 4x2 + -1x3 Reorder the terms: 18 + -2i2 + -1i2x + -3x + -4x2 + x3 = -18 + 3x + 4x2 + -1x3 + 18 + -3x + -4x2 + x3 Reorder the terms: 18 + -2i2 + -1i2x + -3x + -4x2 + x3 = -18 + 18 + 3x + -3x + 4x2 + -4x2 + -1x3 + x3 Combine like terms: -18 + 18 = 0 18 + -2i2 + -1i2x + -3x + -4x2 + x3 = 0 + 3x + -3x + 4x2 + -4x2 + -1x3 + x3 18 + -2i2 + -1i2x + -3x + -4x2 + x3 = 3x + -3x + 4x2 + -4x2 + -1x3 + x3 Combine like terms: 3x + -3x = 0 18 + -2i2 + -1i2x + -3x + -4x2 + x3 = 0 + 4x2 + -4x2 + -1x3 + x3 18 + -2i2 + -1i2x + -3x + -4x2 + x3 = 4x2 + -4x2 + -1x3 + x3 Combine like terms: 4x2 + -4x2 = 0 18 + -2i2 + -1i2x + -3x + -4x2 + x3 = 0 + -1x3 + x3 18 + -2i2 + -1i2x + -3x + -4x2 + x3 = -1x3 + x3 Combine like terms: -1x3 + x3 = 0 18 + -2i2 + -1i2x + -3x + -4x2 + x3 = 0 The solution to this equation could not be determined.
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