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Simplifying (x + -2)(x + -3 + i)(x + -3 + -1i) = 0 Reorder the terms: (-2 + x)(x + -3 + i)(x + -3 + -1i) = 0 Reorder the terms: (-2 + x)(-3 + i + x)(x + -3 + -1i) = 0 Reorder the terms: (-2 + x)(-3 + i + x)(-3 + -1i + x) = 0 Multiply (-2 + x) * (-3 + i + x) (-2(-3 + i + x) + x(-3 + i + x))(-3 + -1i + x) = 0 ((-3 * -2 + i * -2 + x * -2) + x(-3 + i + x))(-3 + -1i + x) = 0 ((6 + -2i + -2x) + x(-3 + i + x))(-3 + -1i + x) = 0 (6 + -2i + -2x + (-3 * x + i * x + x * x))(-3 + -1i + x) = 0 Reorder the terms: (6 + -2i + -2x + (ix + -3x + x2))(-3 + -1i + x) = 0 (6 + -2i + -2x + (ix + -3x + x2))(-3 + -1i + x) = 0 Reorder the terms: (6 + -2i + ix + -2x + -3x + x2)(-3 + -1i + x) = 0 Combine like terms: -2x + -3x = -5x (6 + -2i + ix + -5x + x2)(-3 + -1i + x) = 0 Multiply (6 + -2i + ix + -5x + x2) * (-3 + -1i + x) (6(-3 + -1i + x) + -2i * (-3 + -1i + x) + ix(-3 + -1i + x) + -5x * (-3 + -1i + x) + x2(-3 + -1i + x)) = 0 ((-3 * 6 + -1i * 6 + x * 6) + -2i * (-3 + -1i + x) + ix(-3 + -1i + x) + -5x * (-3 + -1i + x) + x2(-3 + -1i + x)) = 0 ((-18 + -6i + 6x) + -2i * (-3 + -1i + x) + ix(-3 + -1i + x) + -5x * (-3 + -1i + x) + x2(-3 + -1i + x)) = 0 (-18 + -6i + 6x + (-3 * -2i + -1i * -2i + x * -2i) + ix(-3 + -1i + x) + -5x * (-3 + -1i + x) + x2(-3 + -1i + x)) = 0 Reorder the terms: (-18 + -6i + 6x + (6i + -2ix + 2i2) + ix(-3 + -1i + x) + -5x * (-3 + -1i + x) + x2(-3 + -1i + x)) = 0 (-18 + -6i + 6x + (6i + -2ix + 2i2) + ix(-3 + -1i + x) + -5x * (-3 + -1i + x) + x2(-3 + -1i + x)) = 0 (-18 + -6i + 6x + 6i + -2ix + 2i2 + (-3 * ix + -1i * ix + x * ix) + -5x * (-3 + -1i + x) + x2(-3 + -1i + x)) = 0 Reorder the terms: (-18 + -6i + 6x + 6i + -2ix + 2i2 + (-3ix + ix2 + -1i2x) + -5x * (-3 + -1i + x) + x2(-3 + -1i + x)) = 0 (-18 + -6i + 6x + 6i + -2ix + 2i2 + (-3ix + ix2 + -1i2x) + -5x * (-3 + -1i + x) + x2(-3 + -1i + x)) = 0 (-18 + -6i + 6x + 6i + -2ix + 2i2 + -3ix + ix2 + -1i2x + (-3 * -5x + -1i * -5x + x * -5x) + x2(-3 + -1i + x)) = 0 Reorder the terms: (-18 + -6i + 6x + 6i + -2ix + 2i2 + -3ix + ix2 + -1i2x + (5ix + 15x + -5x2) + x2(-3 + -1i + x)) = 0 (-18 + -6i + 6x + 6i + -2ix + 2i2 + -3ix + ix2 + -1i2x + (5ix + 15x + -5x2) + x2(-3 + -1i + x)) = 0 (-18 + -6i + 6x + 6i + -2ix + 2i2 + -3ix + ix2 + -1i2x + 5ix + 15x + -5x2 + (-3 * x2 + -1i * x2 + x * x2)) = 0 Reorder the terms: (-18 + -6i + 6x + 6i + -2ix + 2i2 + -3ix + ix2 + -1i2x + 5ix + 15x + -5x2 + (-1ix2 + -3x2 + x3)) = 0 (-18 + -6i + 6x + 6i + -2ix + 2i2 + -3ix + ix2 + -1i2x + 5ix + 15x + -5x2 + (-1ix2 + -3x2 + x3)) = 0 Reorder the terms: (-18 + -6i + 6i + -2ix + -3ix + 5ix + ix2 + -1ix2 + 2i2 + -1i2x + 6x + 15x + -5x2 + -3x2 + x3) = 0 Combine like terms: -6i + 6i = 0 (-18 + 0 + -2ix + -3ix + 5ix + ix2 + -1ix2 + 2i2 + -1i2x + 6x + 15x + -5x2 + -3x2 + x3) = 0 (-18 + -2ix + -3ix + 5ix + ix2 + -1ix2 + 2i2 + -1i2x + 6x + 15x + -5x2 + -3x2 + x3) = 0 Combine like terms: -2ix + -3ix = -5ix (-18 + -5ix + 5ix + ix2 + -1ix2 + 2i2 + -1i2x + 6x + 15x + -5x2 + -3x2 + x3) = 0 Combine like terms: -5ix + 5ix = 0 (-18 + 0 + ix2 + -1ix2 + 2i2 + -1i2x + 6x + 15x + -5x2 + -3x2 + x3) = 0 (-18 + ix2 + -1ix2 + 2i2 + -1i2x + 6x + 15x + -5x2 + -3x2 + x3) = 0 Combine like terms: ix2 + -1ix2 = 0 (-18 + 0 + 2i2 + -1i2x + 6x + 15x + -5x2 + -3x2 + x3) = 0 (-18 + 2i2 + -1i2x + 6x + 15x + -5x2 + -3x2 + x3) = 0 Combine like terms: 6x + 15x = 21x (-18 + 2i2 + -1i2x + 21x + -5x2 + -3x2 + x3) = 0 Combine like terms: -5x2 + -3x2 = -8x2 (-18 + 2i2 + -1i2x + 21x + -8x2 + x3) = 0 Solving -18 + 2i2 + -1i2x + 21x + -8x2 + 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 + 21x + -8x2 + 18 + x3 = 0 + 18 Reorder the terms: -18 + 18 + 2i2 + -1i2x + 21x + -8x2 + x3 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + 2i2 + -1i2x + 21x + -8x2 + x3 = 0 + 18 2i2 + -1i2x + 21x + -8x2 + x3 = 0 + 18 Combine like terms: 0 + 18 = 18 2i2 + -1i2x + 21x + -8x2 + x3 = 18 Add '-21x' to each side of the equation. 2i2 + -1i2x + 21x + -8x2 + -21x + x3 = 18 + -21x Reorder the terms: 2i2 + -1i2x + 21x + -21x + -8x2 + x3 = 18 + -21x Combine like terms: 21x + -21x = 0 2i2 + -1i2x + 0 + -8x2 + x3 = 18 + -21x 2i2 + -1i2x + -8x2 + x3 = 18 + -21x Add '8x2' to each side of the equation. 2i2 + -1i2x + -8x2 + 8x2 + x3 = 18 + -21x + 8x2 Combine like terms: -8x2 + 8x2 = 0 2i2 + -1i2x + 0 + x3 = 18 + -21x + 8x2 2i2 + -1i2x + x3 = 18 + -21x + 8x2 Add '-1x3' to each side of the equation. 2i2 + -1i2x + x3 + -1x3 = 18 + -21x + 8x2 + -1x3 Combine like terms: x3 + -1x3 = 0 2i2 + -1i2x + 0 = 18 + -21x + 8x2 + -1x3 2i2 + -1i2x = 18 + -21x + 8x2 + -1x3 Reorder the terms: -18 + 2i2 + -1i2x + 21x + -8x2 + x3 = 18 + -21x + 8x2 + -1x3 + -18 + 21x + -8x2 + x3 Reorder the terms: -18 + 2i2 + -1i2x + 21x + -8x2 + x3 = 18 + -18 + -21x + 21x + 8x2 + -8x2 + -1x3 + x3 Combine like terms: 18 + -18 = 0 -18 + 2i2 + -1i2x + 21x + -8x2 + x3 = 0 + -21x + 21x + 8x2 + -8x2 + -1x3 + x3 -18 + 2i2 + -1i2x + 21x + -8x2 + x3 = -21x + 21x + 8x2 + -8x2 + -1x3 + x3 Combine like terms: -21x + 21x = 0 -18 + 2i2 + -1i2x + 21x + -8x2 + x3 = 0 + 8x2 + -8x2 + -1x3 + x3 -18 + 2i2 + -1i2x + 21x + -8x2 + x3 = 8x2 + -8x2 + -1x3 + x3 Combine like terms: 8x2 + -8x2 = 0 -18 + 2i2 + -1i2x + 21x + -8x2 + x3 = 0 + -1x3 + x3 -18 + 2i2 + -1i2x + 21x + -8x2 + x3 = -1x3 + x3 Combine like terms: -1x3 + x3 = 0 -18 + 2i2 + -1i2x + 21x + -8x2 + x3 = 0 The solution to this equation could not be determined.
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