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Simplifying (x + 4)(x + -2 + -1i)(x + 2 + -1i) = 0 Reorder the terms: (4 + x)(x + -2 + -1i)(x + 2 + -1i) = 0 Reorder the terms: (4 + x)(-2 + -1i + x)(x + 2 + -1i) = 0 Reorder the terms: (4 + x)(-2 + -1i + x)(2 + -1i + x) = 0 Multiply (4 + x) * (-2 + -1i + x) (4(-2 + -1i + x) + x(-2 + -1i + x))(2 + -1i + x) = 0 ((-2 * 4 + -1i * 4 + x * 4) + x(-2 + -1i + x))(2 + -1i + x) = 0 ((-8 + -4i + 4x) + x(-2 + -1i + x))(2 + -1i + x) = 0 (-8 + -4i + 4x + (-2 * x + -1i * x + x * x))(2 + -1i + x) = 0 Reorder the terms: (-8 + -4i + 4x + (-1ix + -2x + x2))(2 + -1i + x) = 0 (-8 + -4i + 4x + (-1ix + -2x + x2))(2 + -1i + x) = 0 Reorder the terms: (-8 + -4i + -1ix + 4x + -2x + x2)(2 + -1i + x) = 0 Combine like terms: 4x + -2x = 2x (-8 + -4i + -1ix + 2x + x2)(2 + -1i + x) = 0 Multiply (-8 + -4i + -1ix + 2x + x2) * (2 + -1i + x) (-8(2 + -1i + x) + -4i * (2 + -1i + x) + -1ix * (2 + -1i + x) + 2x * (2 + -1i + x) + x2(2 + -1i + x)) = 0 ((2 * -8 + -1i * -8 + x * -8) + -4i * (2 + -1i + x) + -1ix * (2 + -1i + x) + 2x * (2 + -1i + x) + x2(2 + -1i + x)) = 0 ((-16 + 8i + -8x) + -4i * (2 + -1i + x) + -1ix * (2 + -1i + x) + 2x * (2 + -1i + x) + x2(2 + -1i + x)) = 0 (-16 + 8i + -8x + (2 * -4i + -1i * -4i + x * -4i) + -1ix * (2 + -1i + x) + 2x * (2 + -1i + x) + x2(2 + -1i + x)) = 0 Reorder the terms: (-16 + 8i + -8x + (-8i + -4ix + 4i2) + -1ix * (2 + -1i + x) + 2x * (2 + -1i + x) + x2(2 + -1i + x)) = 0 (-16 + 8i + -8x + (-8i + -4ix + 4i2) + -1ix * (2 + -1i + x) + 2x * (2 + -1i + x) + x2(2 + -1i + x)) = 0 (-16 + 8i + -8x + -8i + -4ix + 4i2 + (2 * -1ix + -1i * -1ix + x * -1ix) + 2x * (2 + -1i + x) + x2(2 + -1i + x)) = 0 Reorder the terms: (-16 + 8i + -8x + -8i + -4ix + 4i2 + (-2ix + -1ix2 + 1i2x) + 2x * (2 + -1i + x) + x2(2 + -1i + x)) = 0 (-16 + 8i + -8x + -8i + -4ix + 4i2 + (-2ix + -1ix2 + 1i2x) + 2x * (2 + -1i + x) + x2(2 + -1i + x)) = 0 (-16 + 8i + -8x + -8i + -4ix + 4i2 + -2ix + -1ix2 + 1i2x + (2 * 2x + -1i * 2x + x * 2x) + x2(2 + -1i + x)) = 0 Reorder the terms: (-16 + 8i + -8x + -8i + -4ix + 4i2 + -2ix + -1ix2 + 1i2x + (-2ix + 4x + 2x2) + x2(2 + -1i + x)) = 0 (-16 + 8i + -8x + -8i + -4ix + 4i2 + -2ix + -1ix2 + 1i2x + (-2ix + 4x + 2x2) + x2(2 + -1i + x)) = 0 (-16 + 8i + -8x + -8i + -4ix + 4i2 + -2ix + -1ix2 + 1i2x + -2ix + 4x + 2x2 + (2 * x2 + -1i * x2 + x * x2)) = 0 Reorder the terms: (-16 + 8i + -8x + -8i + -4ix + 4i2 + -2ix + -1ix2 + 1i2x + -2ix + 4x + 2x2 + (-1ix2 + 2x2 + x3)) = 0 (-16 + 8i + -8x + -8i + -4ix + 4i2 + -2ix + -1ix2 + 1i2x + -2ix + 4x + 2x2 + (-1ix2 + 2x2 + x3)) = 0 Reorder the terms: (-16 + 8i + -8i + -4ix + -2ix + -2ix + -1ix2 + -1ix2 + 4i2 + 1i2x + -8x + 4x + 2x2 + 2x2 + x3) = 0 Combine like terms: 8i + -8i = 0 (-16 + 0 + -4ix + -2ix + -2ix + -1ix2 + -1ix2 + 4i2 + 1i2x + -8x + 4x + 2x2 + 2x2 + x3) = 0 (-16 + -4ix + -2ix + -2ix + -1ix2 + -1ix2 + 4i2 + 1i2x + -8x + 4x + 2x2 + 2x2 + x3) = 0 Combine like terms: -4ix + -2ix = -6ix (-16 + -6ix + -2ix + -1ix2 + -1ix2 + 4i2 + 1i2x + -8x + 4x + 2x2 + 2x2 + x3) = 0 Combine like terms: -6ix + -2ix = -8ix (-16 + -8ix + -1ix2 + -1ix2 + 4i2 + 1i2x + -8x + 4x + 2x2 + 2x2 + x3) = 0 Combine like terms: -1ix2 + -1ix2 = -2ix2 (-16 + -8ix + -2ix2 + 4i2 + 1i2x + -8x + 4x + 2x2 + 2x2 + x3) = 0 Combine like terms: -8x + 4x = -4x (-16 + -8ix + -2ix2 + 4i2 + 1i2x + -4x + 2x2 + 2x2 + x3) = 0 Combine like terms: 2x2 + 2x2 = 4x2 (-16 + -8ix + -2ix2 + 4i2 + 1i2x + -4x + 4x2 + x3) = 0 Solving -16 + -8ix + -2ix2 + 4i2 + 1i2x + -4x + 4x2 + x3 = 0 Solving for variable 'i'. The solution to this equation could not be determined.
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