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Simplifying (x + -2 + i)(x + -2 + -1i)(x + 3) = 0 Reorder the terms: (-2 + i + x)(x + -2 + -1i)(x + 3) = 0 Reorder the terms: (-2 + i + x)(-2 + -1i + x)(x + 3) = 0 Reorder the terms: (-2 + i + x)(-2 + -1i + x)(3 + x) = 0 Multiply (-2 + i + x) * (-2 + -1i + x) (-2(-2 + -1i + x) + i(-2 + -1i + x) + x(-2 + -1i + x))(3 + x) = 0 ((-2 * -2 + -1i * -2 + x * -2) + i(-2 + -1i + x) + x(-2 + -1i + x))(3 + x) = 0 ((4 + 2i + -2x) + i(-2 + -1i + x) + x(-2 + -1i + x))(3 + x) = 0 (4 + 2i + -2x + (-2 * i + -1i * i + x * i) + x(-2 + -1i + x))(3 + x) = 0 Reorder the terms: (4 + 2i + -2x + (-2i + ix + -1i2) + x(-2 + -1i + x))(3 + x) = 0 (4 + 2i + -2x + (-2i + ix + -1i2) + x(-2 + -1i + x))(3 + x) = 0 (4 + 2i + -2x + -2i + ix + -1i2 + (-2 * x + -1i * x + x * x))(3 + x) = 0 Reorder the terms: (4 + 2i + -2x + -2i + ix + -1i2 + (-1ix + -2x + x2))(3 + x) = 0 (4 + 2i + -2x + -2i + ix + -1i2 + (-1ix + -2x + x2))(3 + x) = 0 Reorder the terms: (4 + 2i + -2i + ix + -1ix + -1i2 + -2x + -2x + x2)(3 + x) = 0 Combine like terms: 2i + -2i = 0 (4 + 0 + ix + -1ix + -1i2 + -2x + -2x + x2)(3 + x) = 0 (4 + ix + -1ix + -1i2 + -2x + -2x + x2)(3 + x) = 0 Combine like terms: ix + -1ix = 0 (4 + 0 + -1i2 + -2x + -2x + x2)(3 + x) = 0 (4 + -1i2 + -2x + -2x + x2)(3 + x) = 0 Combine like terms: -2x + -2x = -4x (4 + -1i2 + -4x + x2)(3 + x) = 0 Multiply (4 + -1i2 + -4x + x2) * (3 + x) (4(3 + x) + -1i2 * (3 + x) + -4x * (3 + x) + x2(3 + x)) = 0 ((3 * 4 + x * 4) + -1i2 * (3 + x) + -4x * (3 + x) + x2(3 + x)) = 0 ((12 + 4x) + -1i2 * (3 + x) + -4x * (3 + x) + x2(3 + x)) = 0 (12 + 4x + (3 * -1i2 + x * -1i2) + -4x * (3 + x) + x2(3 + x)) = 0 (12 + 4x + (-3i2 + -1i2x) + -4x * (3 + x) + x2(3 + x)) = 0 (12 + 4x + -3i2 + -1i2x + (3 * -4x + x * -4x) + x2(3 + x)) = 0 (12 + 4x + -3i2 + -1i2x + (-12x + -4x2) + x2(3 + x)) = 0 (12 + 4x + -3i2 + -1i2x + -12x + -4x2 + (3 * x2 + x * x2)) = 0 (12 + 4x + -3i2 + -1i2x + -12x + -4x2 + (3x2 + x3)) = 0 Reorder the terms: (12 + -3i2 + -1i2x + 4x + -12x + -4x2 + 3x2 + x3) = 0 Combine like terms: 4x + -12x = -8x (12 + -3i2 + -1i2x + -8x + -4x2 + 3x2 + x3) = 0 Combine like terms: -4x2 + 3x2 = -1x2 (12 + -3i2 + -1i2x + -8x + -1x2 + x3) = 0 Solving 12 + -3i2 + -1i2x + -8x + -1x2 + x3 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -3i2 + -1i2x + -8x + -1x2 + -12 + x3 = 0 + -12 Reorder the terms: 12 + -12 + -3i2 + -1i2x + -8x + -1x2 + x3 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -3i2 + -1i2x + -8x + -1x2 + x3 = 0 + -12 -3i2 + -1i2x + -8x + -1x2 + x3 = 0 + -12 Combine like terms: 0 + -12 = -12 -3i2 + -1i2x + -8x + -1x2 + x3 = -12 Add '8x' to each side of the equation. -3i2 + -1i2x + -8x + -1x2 + 8x + x3 = -12 + 8x Reorder the terms: -3i2 + -1i2x + -8x + 8x + -1x2 + x3 = -12 + 8x Combine like terms: -8x + 8x = 0 -3i2 + -1i2x + 0 + -1x2 + x3 = -12 + 8x -3i2 + -1i2x + -1x2 + x3 = -12 + 8x Add 'x2' to each side of the equation. -3i2 + -1i2x + -1x2 + x2 + x3 = -12 + 8x + x2 Combine like terms: -1x2 + x2 = 0 -3i2 + -1i2x + 0 + x3 = -12 + 8x + x2 -3i2 + -1i2x + x3 = -12 + 8x + x2 Add '-1x3' to each side of the equation. -3i2 + -1i2x + x3 + -1x3 = -12 + 8x + x2 + -1x3 Combine like terms: x3 + -1x3 = 0 -3i2 + -1i2x + 0 = -12 + 8x + x2 + -1x3 -3i2 + -1i2x = -12 + 8x + x2 + -1x3 Reorder the terms: 12 + -3i2 + -1i2x + -8x + -1x2 + x3 = -12 + 8x + x2 + -1x3 + 12 + -8x + -1x2 + x3 Reorder the terms: 12 + -3i2 + -1i2x + -8x + -1x2 + x3 = -12 + 12 + 8x + -8x + x2 + -1x2 + -1x3 + x3 Combine like terms: -12 + 12 = 0 12 + -3i2 + -1i2x + -8x + -1x2 + x3 = 0 + 8x + -8x + x2 + -1x2 + -1x3 + x3 12 + -3i2 + -1i2x + -8x + -1x2 + x3 = 8x + -8x + x2 + -1x2 + -1x3 + x3 Combine like terms: 8x + -8x = 0 12 + -3i2 + -1i2x + -8x + -1x2 + x3 = 0 + x2 + -1x2 + -1x3 + x3 12 + -3i2 + -1i2x + -8x + -1x2 + x3 = x2 + -1x2 + -1x3 + x3 Combine like terms: x2 + -1x2 = 0 12 + -3i2 + -1i2x + -8x + -1x2 + x3 = 0 + -1x3 + x3 12 + -3i2 + -1i2x + -8x + -1x2 + x3 = -1x3 + x3 Combine like terms: -1x3 + x3 = 0 12 + -3i2 + -1i2x + -8x + -1x2 + x3 = 0 The solution to this equation could not be determined.
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