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Simplifying (x + 2)(3 + -2i)(3 + 2i)(2 + 3i)(2 + -3i) = 0 Reorder the terms: (2 + x)(3 + -2i)(3 + 2i)(2 + 3i)(2 + -3i) = 0 Multiply (2 + x) * (3 + -2i) (2(3 + -2i) + x(3 + -2i))(3 + 2i)(2 + 3i)(2 + -3i) = 0 ((3 * 2 + -2i * 2) + x(3 + -2i))(3 + 2i)(2 + 3i)(2 + -3i) = 0 ((6 + -4i) + x(3 + -2i))(3 + 2i)(2 + 3i)(2 + -3i) = 0 (6 + -4i + (3 * x + -2i * x))(3 + 2i)(2 + 3i)(2 + -3i) = 0 Reorder the terms: (6 + -4i + (-2ix + 3x))(3 + 2i)(2 + 3i)(2 + -3i) = 0 (6 + -4i + (-2ix + 3x))(3 + 2i)(2 + 3i)(2 + -3i) = 0 (6 + -4i + -2ix + 3x)(3 + 2i)(2 + 3i)(2 + -3i) = 0 Multiply (6 + -4i + -2ix + 3x) * (3 + 2i) (6(3 + 2i) + -4i * (3 + 2i) + -2ix * (3 + 2i) + 3x * (3 + 2i))(2 + 3i)(2 + -3i) = 0 ((3 * 6 + 2i * 6) + -4i * (3 + 2i) + -2ix * (3 + 2i) + 3x * (3 + 2i))(2 + 3i)(2 + -3i) = 0 ((18 + 12i) + -4i * (3 + 2i) + -2ix * (3 + 2i) + 3x * (3 + 2i))(2 + 3i)(2 + -3i) = 0 (18 + 12i + (3 * -4i + 2i * -4i) + -2ix * (3 + 2i) + 3x * (3 + 2i))(2 + 3i)(2 + -3i) = 0 (18 + 12i + (-12i + -8i2) + -2ix * (3 + 2i) + 3x * (3 + 2i))(2 + 3i)(2 + -3i) = 0 (18 + 12i + -12i + -8i2 + (3 * -2ix + 2i * -2ix) + 3x * (3 + 2i))(2 + 3i)(2 + -3i) = 0 (18 + 12i + -12i + -8i2 + (-6ix + -4i2x) + 3x * (3 + 2i))(2 + 3i)(2 + -3i) = 0 (18 + 12i + -12i + -8i2 + -6ix + -4i2x + (3 * 3x + 2i * 3x))(2 + 3i)(2 + -3i) = 0 Reorder the terms: (18 + 12i + -12i + -8i2 + -6ix + -4i2x + (6ix + 9x))(2 + 3i)(2 + -3i) = 0 (18 + 12i + -12i + -8i2 + -6ix + -4i2x + (6ix + 9x))(2 + 3i)(2 + -3i) = 0 Reorder the terms: (18 + 12i + -12i + -6ix + 6ix + -8i2 + -4i2x + 9x)(2 + 3i)(2 + -3i) = 0 Combine like terms: 12i + -12i = 0 (18 + 0 + -6ix + 6ix + -8i2 + -4i2x + 9x)(2 + 3i)(2 + -3i) = 0 (18 + -6ix + 6ix + -8i2 + -4i2x + 9x)(2 + 3i)(2 + -3i) = 0 Combine like terms: -6ix + 6ix = 0 (18 + 0 + -8i2 + -4i2x + 9x)(2 + 3i)(2 + -3i) = 0 (18 + -8i2 + -4i2x + 9x)(2 + 3i)(2 + -3i) = 0 Multiply (18 + -8i2 + -4i2x + 9x) * (2 + 3i) (18(2 + 3i) + -8i2 * (2 + 3i) + -4i2x * (2 + 3i) + 9x * (2 + 3i))(2 + -3i) = 0 ((2 * 18 + 3i * 18) + -8i2 * (2 + 3i) + -4i2x * (2 + 3i) + 9x * (2 + 3i))(2 + -3i) = 0 ((36 + 54i) + -8i2 * (2 + 3i) + -4i2x * (2 + 3i) + 9x * (2 + 3i))(2 + -3i) = 0 (36 + 54i + (2 * -8i2 + 3i * -8i2) + -4i2x * (2 + 3i) + 9x * (2 + 3i))(2 + -3i) = 0 (36 + 54i + (-16i2 + -24i3) + -4i2x * (2 + 3i) + 9x * (2 + 3i))(2 + -3i) = 0 (36 + 54i + -16i2 + -24i3 + (2 * -4i2x + 3i * -4i2x) + 9x * (2 + 3i))(2 + -3i) = 0 (36 + 54i + -16i2 + -24i3 + (-8i2x + -12i3x) + 9x * (2 + 3i))(2 + -3i) = 0 (36 + 54i + -16i2 + -24i3 + -8i2x + -12i3x + (2 * 9x + 3i * 9x))(2 + -3i) = 0 Reorder the terms: (36 + 54i + -16i2 + -24i3 + -8i2x + -12i3x + (27ix + 18x))(2 + -3i) = 0 (36 + 54i + -16i2 + -24i3 + -8i2x + -12i3x + (27ix + 18x))(2 + -3i) = 0 Reorder the terms: (36 + 54i + 27ix + -16i2 + -8i2x + -24i3 + -12i3x + 18x)(2 + -3i) = 0 (36 + 54i + 27ix + -16i2 + -8i2x + -24i3 + -12i3x + 18x)(2 + -3i) = 0 Multiply (36 + 54i + 27ix + -16i2 + -8i2x + -24i3 + -12i3x + 18x) * (2 + -3i) (36(2 + -3i) + 54i * (2 + -3i) + 27ix * (2 + -3i) + -16i2 * (2 + -3i) + -8i2x * (2 + -3i) + -24i3 * (2 + -3i) + -12i3x * (2 + -3i) + 18x * (2 + -3i)) = 0 ((2 * 36 + -3i * 36) + 54i * (2 + -3i) + 27ix * (2 + -3i) + -16i2 * (2 + -3i) + -8i2x * (2 + -3i) + -24i3 * (2 + -3i) + -12i3x * (2 + -3i) + 18x * (2 + -3i)) = 0 ((72 + -108i) + 54i * (2 + -3i) + 27ix * (2 + -3i) + -16i2 * (2 + -3i) + -8i2x * (2 + -3i) + -24i3 * (2 + -3i) + -12i3x * (2 + -3i) + 18x * (2 + -3i)) = 0 (72 + -108i + (2 * 54i + -3i * 54i) + 27ix * (2 + -3i) + -16i2 * (2 + -3i) + -8i2x * (2 + -3i) + -24i3 * (2 + -3i) + -12i3x * (2 + -3i) + 18x * (2 + -3i)) = 0 (72 + -108i + (108i + -162i2) + 27ix * (2 + -3i) + -16i2 * (2 + -3i) + -8i2x * (2 + -3i) + -24i3 * (2 + -3i) + -12i3x * (2 + -3i) + 18x * (2 + -3i)) = 0 (72 + -108i + 108i + -162i2 + (2 * 27ix + -3i * 27ix) + -16i2 * (2 + -3i) + -8i2x * (2 + -3i) + -24i3 * (2 + -3i) + -12i3x * (2 + -3i) + 18x * (2 + -3i)) = 0 (72 + -108i + 108i + -162i2 + (54ix + -81i2x) + -16i2 * (2 + -3i) + -8i2x * (2 + -3i) + -24i3 * (2 + -3i) + -12i3x * (2 + -3i) + 18x * (2 + -3i)) = 0 (72 + -108i + 108i + -162i2 + 54ix + -81i2x + (2 * -16i2 + -3i * -16i2) + -8i2x * (2 + -3i) + -24i3 * (2 + -3i) + -12i3x * (2 + -3i) + 18x * (2 + -3i)) = 0 (72 + -108i + 108i + -162i2 + 54ix + -81i2x + (-32i2 + 48i3) + -8i2x * (2 + -3i) + -24i3 * (2 + -3i) + -12i3x * (2 + -3i) + 18x * (2 + -3i)) = 0 (72 + -108i + 108i + -162i2 + 54ix + -81i2x + -32i2 + 48i3 + (2 * -8i2x + -3i * -8i2x) + -24i3 * (2 + -3i) + -12i3x * (2 + -3i) + 18x * (2 + -3i)) = 0 (72 + -108i + 108i + -162i2 + 54ix + -81i2x + -32i2 + 48i3 + (-16i2x + 24i3x) + -24i3 * (2 + -3i) + -12i3x * (2 + -3i) + 18x * (2 + -3i)) = 0 (72 + -108i + 108i + -162i2 + 54ix + -81i2x + -32i2 + 48i3 + -16i2x + 24i3x + (2 * -24i3 + -3i * -24i3) + -12i3x * (2 + -3i) + 18x * (2 + -3i)) = 0 (72 + -108i + 108i + -162i2 + 54ix + -81i2x + -32i2 + 48i3 + -16i2x + 24i3x + (-48i3 + 72i4) + -12i3x * (2 + -3i) + 18x * (2 + -3i)) = 0 (72 + -108i + 108i + -162i2 + 54ix + -81i2x + -32i2 + 48i3 + -16i2x + 24i3x + -48i3 + 72i4 + (2 * -12i3x + -3i * -12i3x) + 18x * (2 + -3i)) = 0 (72 + -108i + 108i + -162i2 + 54ix + -81i2x + -32i2 + 48i3 + -16i2x + 24i3x + -48i3 + 72i4 + (-24i3x + 36i4x) + 18x * (2 + -3i)) = 0 (72 + -108i + 108i + -162i2 + 54ix + -81i2x + -32i2 + 48i3 + -16i2x + 24i3x + -48i3 + 72i4 + -24i3x + 36i4x + (2 * 18x + -3i * 18x)) = 0 Reorder the terms: (72 + -108i + 108i + -162i2 + 54ix + -81i2x + -32i2 + 48i3 + -16i2x + 24i3x + -48i3 + 72i4 + -24i3x + 36i4x + (-54ix + 36x)) = 0 (72 + -108i + 108i + -162i2 + 54ix + -81i2x + -32i2 + 48i3 + -16i2x + 24i3x + -48i3 + 72i4 + -24i3x + 36i4x + (-54ix + 36x)) = 0 Reorder the terms: (72 + -108i + 108i + 54ix + -54ix + -162i2 + -32i2 + -81i2x + -16i2x + 48i3 + -48i3 + 24i3x + -24i3x + 72i4 + 36i4x + 36x) = 0 Combine like terms: -108i + 108i = 0 (72 + 0 + 54ix + -54ix + -162i2 + -32i2 + -81i2x + -16i2x + 48i3 + -48i3 + 24i3x + -24i3x + 72i4 + 36i4x + 36x) = 0 (72 + 54ix + -54ix + -162i2 + -32i2 + -81i2x + -16i2x + 48i3 + -48i3 + 24i3x + -24i3x + 72i4 + 36i4x + 36x) = 0 Combine like terms: 54ix + -54ix = 0 (72 + 0 + -162i2 + -32i2 + -81i2x + -16i2x + 48i3 + -48i3 + 24i3x + -24i3x + 72i4 + 36i4x + 36x) = 0 (72 + -162i2 + -32i2 + -81i2x + -16i2x + 48i3 + -48i3 + 24i3x + -24i3x + 72i4 + 36i4x + 36x) = 0 Combine like terms: -162i2 + -32i2 = -194i2 (72 + -194i2 + -81i2x + -16i2x + 48i3 + -48i3 + 24i3x + -24i3x + 72i4 + 36i4x + 36x) = 0 Combine like terms: -81i2x + -16i2x = -97i2x (72 + -194i2 + -97i2x + 48i3 + -48i3 + 24i3x + -24i3x + 72i4 + 36i4x + 36x) = 0 Combine like terms: 48i3 + -48i3 = 0 (72 + -194i2 + -97i2x + 0 + 24i3x + -24i3x + 72i4 + 36i4x + 36x) = 0 (72 + -194i2 + -97i2x + 24i3x + -24i3x + 72i4 + 36i4x + 36x) = 0 Combine like terms: 24i3x + -24i3x = 0 (72 + -194i2 + -97i2x + 0 + 72i4 + 36i4x + 36x) = 0 (72 + -194i2 + -97i2x + 72i4 + 36i4x + 36x) = 0 Solving 72 + -194i2 + -97i2x + 72i4 + 36i4x + 36x = 0 Solving for variable 'i'. The solution to this equation could not be determined.
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