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Simplifying (x + -3 + -2i)(x + -3 + 2i)(x + 2)(x + -1) = 0 Reorder the terms: (-3 + -2i + x)(x + -3 + 2i)(x + 2)(x + -1) = 0 Reorder the terms: (-3 + -2i + x)(-3 + 2i + x)(x + 2)(x + -1) = 0 Reorder the terms: (-3 + -2i + x)(-3 + 2i + x)(2 + x)(x + -1) = 0 Reorder the terms: (-3 + -2i + x)(-3 + 2i + x)(2 + x)(-1 + x) = 0 Multiply (-3 + -2i + x) * (-3 + 2i + x) (-3(-3 + 2i + x) + -2i * (-3 + 2i + x) + x(-3 + 2i + x))(2 + x)(-1 + x) = 0 ((-3 * -3 + 2i * -3 + x * -3) + -2i * (-3 + 2i + x) + x(-3 + 2i + x))(2 + x)(-1 + x) = 0 ((9 + -6i + -3x) + -2i * (-3 + 2i + x) + x(-3 + 2i + x))(2 + x)(-1 + x) = 0 (9 + -6i + -3x + (-3 * -2i + 2i * -2i + x * -2i) + x(-3 + 2i + x))(2 + x)(-1 + x) = 0 Reorder the terms: (9 + -6i + -3x + (6i + -2ix + -4i2) + x(-3 + 2i + x))(2 + x)(-1 + x) = 0 (9 + -6i + -3x + (6i + -2ix + -4i2) + x(-3 + 2i + x))(2 + x)(-1 + x) = 0 (9 + -6i + -3x + 6i + -2ix + -4i2 + (-3 * x + 2i * x + x * x))(2 + x)(-1 + x) = 0 Reorder the terms: (9 + -6i + -3x + 6i + -2ix + -4i2 + (2ix + -3x + x2))(2 + x)(-1 + x) = 0 (9 + -6i + -3x + 6i + -2ix + -4i2 + (2ix + -3x + x2))(2 + x)(-1 + x) = 0 Reorder the terms: (9 + -6i + 6i + -2ix + 2ix + -4i2 + -3x + -3x + x2)(2 + x)(-1 + x) = 0 Combine like terms: -6i + 6i = 0 (9 + 0 + -2ix + 2ix + -4i2 + -3x + -3x + x2)(2 + x)(-1 + x) = 0 (9 + -2ix + 2ix + -4i2 + -3x + -3x + x2)(2 + x)(-1 + x) = 0 Combine like terms: -2ix + 2ix = 0 (9 + 0 + -4i2 + -3x + -3x + x2)(2 + x)(-1 + x) = 0 (9 + -4i2 + -3x + -3x + x2)(2 + x)(-1 + x) = 0 Combine like terms: -3x + -3x = -6x (9 + -4i2 + -6x + x2)(2 + x)(-1 + x) = 0 Multiply (9 + -4i2 + -6x + x2) * (2 + x) (9(2 + x) + -4i2 * (2 + x) + -6x * (2 + x) + x2(2 + x))(-1 + x) = 0 ((2 * 9 + x * 9) + -4i2 * (2 + x) + -6x * (2 + x) + x2(2 + x))(-1 + x) = 0 ((18 + 9x) + -4i2 * (2 + x) + -6x * (2 + x) + x2(2 + x))(-1 + x) = 0 (18 + 9x + (2 * -4i2 + x * -4i2) + -6x * (2 + x) + x2(2 + x))(-1 + x) = 0 (18 + 9x + (-8i2 + -4i2x) + -6x * (2 + x) + x2(2 + x))(-1 + x) = 0 (18 + 9x + -8i2 + -4i2x + (2 * -6x + x * -6x) + x2(2 + x))(-1 + x) = 0 (18 + 9x + -8i2 + -4i2x + (-12x + -6x2) + x2(2 + x))(-1 + x) = 0 (18 + 9x + -8i2 + -4i2x + -12x + -6x2 + (2 * x2 + x * x2))(-1 + x) = 0 (18 + 9x + -8i2 + -4i2x + -12x + -6x2 + (2x2 + x3))(-1 + x) = 0 Reorder the terms: (18 + -8i2 + -4i2x + 9x + -12x + -6x2 + 2x2 + x3)(-1 + x) = 0 Combine like terms: 9x + -12x = -3x (18 + -8i2 + -4i2x + -3x + -6x2 + 2x2 + x3)(-1 + x) = 0 Combine like terms: -6x2 + 2x2 = -4x2 (18 + -8i2 + -4i2x + -3x + -4x2 + x3)(-1 + x) = 0 Multiply (18 + -8i2 + -4i2x + -3x + -4x2 + x3) * (-1 + x) (18(-1 + x) + -8i2 * (-1 + x) + -4i2x * (-1 + x) + -3x * (-1 + x) + -4x2 * (-1 + x) + x3(-1 + x)) = 0 ((-1 * 18 + x * 18) + -8i2 * (-1 + x) + -4i2x * (-1 + x) + -3x * (-1 + x) + -4x2 * (-1 + x) + x3(-1 + x)) = 0 ((-18 + 18x) + -8i2 * (-1 + x) + -4i2x * (-1 + x) + -3x * (-1 + x) + -4x2 * (-1 + x) + x3(-1 + x)) = 0 (-18 + 18x + (-1 * -8i2 + x * -8i2) + -4i2x * (-1 + x) + -3x * (-1 + x) + -4x2 * (-1 + x) + x3(-1 + x)) = 0 (-18 + 18x + (8i2 + -8i2x) + -4i2x * (-1 + x) + -3x * (-1 + x) + -4x2 * (-1 + x) + x3(-1 + x)) = 0 (-18 + 18x + 8i2 + -8i2x + (-1 * -4i2x + x * -4i2x) + -3x * (-1 + x) + -4x2 * (-1 + x) + x3(-1 + x)) = 0 (-18 + 18x + 8i2 + -8i2x + (4i2x + -4i2x2) + -3x * (-1 + x) + -4x2 * (-1 + x) + x3(-1 + x)) = 0 (-18 + 18x + 8i2 + -8i2x + 4i2x + -4i2x2 + (-1 * -3x + x * -3x) + -4x2 * (-1 + x) + x3(-1 + x)) = 0 (-18 + 18x + 8i2 + -8i2x + 4i2x + -4i2x2 + (3x + -3x2) + -4x2 * (-1 + x) + x3(-1 + x)) = 0 (-18 + 18x + 8i2 + -8i2x + 4i2x + -4i2x2 + 3x + -3x2 + (-1 * -4x2 + x * -4x2) + x3(-1 + x)) = 0 (-18 + 18x + 8i2 + -8i2x + 4i2x + -4i2x2 + 3x + -3x2 + (4x2 + -4x3) + x3(-1 + x)) = 0 (-18 + 18x + 8i2 + -8i2x + 4i2x + -4i2x2 + 3x + -3x2 + 4x2 + -4x3 + (-1 * x3 + x * x3)) = 0 (-18 + 18x + 8i2 + -8i2x + 4i2x + -4i2x2 + 3x + -3x2 + 4x2 + -4x3 + (-1x3 + x4)) = 0 Reorder the terms: (-18 + 8i2 + -8i2x + 4i2x + -4i2x2 + 18x + 3x + -3x2 + 4x2 + -4x3 + -1x3 + x4) = 0 Combine like terms: -8i2x + 4i2x = -4i2x (-18 + 8i2 + -4i2x + -4i2x2 + 18x + 3x + -3x2 + 4x2 + -4x3 + -1x3 + x4) = 0 Combine like terms: 18x + 3x = 21x (-18 + 8i2 + -4i2x + -4i2x2 + 21x + -3x2 + 4x2 + -4x3 + -1x3 + x4) = 0 Combine like terms: -3x2 + 4x2 = 1x2 (-18 + 8i2 + -4i2x + -4i2x2 + 21x + 1x2 + -4x3 + -1x3 + x4) = 0 Combine like terms: -4x3 + -1x3 = -5x3 (-18 + 8i2 + -4i2x + -4i2x2 + 21x + 1x2 + -5x3 + x4) = 0 Solving -18 + 8i2 + -4i2x + -4i2x2 + 21x + 1x2 + -5x3 + x4 = 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 + 8i2 + -4i2x + -4i2x2 + 21x + 1x2 + -5x3 + 18 + x4 = 0 + 18 Reorder the terms: -18 + 18 + 8i2 + -4i2x + -4i2x2 + 21x + 1x2 + -5x3 + x4 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + 8i2 + -4i2x + -4i2x2 + 21x + 1x2 + -5x3 + x4 = 0 + 18 8i2 + -4i2x + -4i2x2 + 21x + 1x2 + -5x3 + x4 = 0 + 18 Combine like terms: 0 + 18 = 18 8i2 + -4i2x + -4i2x2 + 21x + 1x2 + -5x3 + x4 = 18 Add '-21x' to each side of the equation. 8i2 + -4i2x + -4i2x2 + 21x + 1x2 + -5x3 + -21x + x4 = 18 + -21x Reorder the terms: 8i2 + -4i2x + -4i2x2 + 21x + -21x + 1x2 + -5x3 + x4 = 18 + -21x Combine like terms: 21x + -21x = 0 8i2 + -4i2x + -4i2x2 + 0 + 1x2 + -5x3 + x4 = 18 + -21x 8i2 + -4i2x + -4i2x2 + 1x2 + -5x3 + x4 = 18 + -21x Add '-1x2' to each side of the equation. 8i2 + -4i2x + -4i2x2 + 1x2 + -5x3 + -1x2 + x4 = 18 + -21x + -1x2 Reorder the terms: 8i2 + -4i2x + -4i2x2 + 1x2 + -1x2 + -5x3 + x4 = 18 + -21x + -1x2 Combine like terms: 1x2 + -1x2 = 0 8i2 + -4i2x + -4i2x2 + 0 + -5x3 + x4 = 18 + -21x + -1x2 8i2 + -4i2x + -4i2x2 + -5x3 + x4 = 18 + -21x + -1x2 Add '5x3' to each side of the equation. 8i2 + -4i2x + -4i2x2 + -5x3 + 5x3 + x4 = 18 + -21x + -1x2 + 5x3 Combine like terms: -5x3 + 5x3 = 0 8i2 + -4i2x + -4i2x2 + 0 + x4 = 18 + -21x + -1x2 + 5x3 8i2 + -4i2x + -4i2x2 + x4 = 18 + -21x + -1x2 + 5x3 Add '-1x4' to each side of the equation. 8i2 + -4i2x + -4i2x2 + x4 + -1x4 = 18 + -21x + -1x2 + 5x3 + -1x4 Combine like terms: x4 + -1x4 = 0 8i2 + -4i2x + -4i2x2 + 0 = 18 + -21x + -1x2 + 5x3 + -1x4 8i2 + -4i2x + -4i2x2 = 18 + -21x + -1x2 + 5x3 + -1x4 Reorder the terms: -18 + 8i2 + -4i2x + -4i2x2 + 21x + x2 + -5x3 + x4 = 18 + -21x + -1x2 + 5x3 + -1x4 + -18 + 21x + x2 + -5x3 + x4 Reorder the terms: -18 + 8i2 + -4i2x + -4i2x2 + 21x + x2 + -5x3 + x4 = 18 + -18 + -21x + 21x + -1x2 + x2 + 5x3 + -5x3 + -1x4 + x4 Combine like terms: 18 + -18 = 0 -18 + 8i2 + -4i2x + -4i2x2 + 21x + x2 + -5x3 + x4 = 0 + -21x + 21x + -1x2 + x2 + 5x3 + -5x3 + -1x4 + x4 -18 + 8i2 + -4i2x + -4i2x2 + 21x + x2 + -5x3 + x4 = -21x + 21x + -1x2 + x2 + 5x3 + -5x3 + -1x4 + x4 Combine like terms: -21x + 21x = 0 -18 + 8i2 + -4i2x + -4i2x2 + 21x + x2 + -5x3 + x4 = 0 + -1x2 + x2 + 5x3 + -5x3 + -1x4 + x4 -18 + 8i2 + -4i2x + -4i2x2 + 21x + x2 + -5x3 + x4 = -1x2 + x2 + 5x3 + -5x3 + -1x4 + x4 Combine like terms: -1x2 + x2 = 0 -18 + 8i2 + -4i2x + -4i2x2 + 21x + x2 + -5x3 + x4 = 0 + 5x3 + -5x3 + -1x4 + x4 -18 + 8i2 + -4i2x + -4i2x2 + 21x + x2 + -5x3 + x4 = 5x3 + -5x3 + -1x4 + x4 Combine like terms: 5x3 + -5x3 = 0 -18 + 8i2 + -4i2x + -4i2x2 + 21x + x2 + -5x3 + x4 = 0 + -1x4 + x4 -18 + 8i2 + -4i2x + -4i2x2 + 21x + x2 + -5x3 + x4 = -1x4 + x4 Combine like terms: -1x4 + x4 = 0 -18 + 8i2 + -4i2x + -4i2x2 + 21x + x2 + -5x3 + x4 = 0 The solution to this equation could not be determined.
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