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Simplifying (x + 1)(x + -3)(x + -3 + -2i)(x + -3 + 2i) = 0 Reorder the terms: (1 + x)(x + -3)(x + -3 + -2i)(x + -3 + 2i) = 0 Reorder the terms: (1 + x)(-3 + x)(x + -3 + -2i)(x + -3 + 2i) = 0 Reorder the terms: (1 + x)(-3 + x)(-3 + -2i + x)(x + -3 + 2i) = 0 Reorder the terms: (1 + x)(-3 + x)(-3 + -2i + x)(-3 + 2i + x) = 0 Multiply (1 + x) * (-3 + x) (1(-3 + x) + x(-3 + x))(-3 + -2i + x)(-3 + 2i + x) = 0 ((-3 * 1 + x * 1) + x(-3 + x))(-3 + -2i + x)(-3 + 2i + x) = 0 ((-3 + 1x) + x(-3 + x))(-3 + -2i + x)(-3 + 2i + x) = 0 (-3 + 1x + (-3 * x + x * x))(-3 + -2i + x)(-3 + 2i + x) = 0 (-3 + 1x + (-3x + x2))(-3 + -2i + x)(-3 + 2i + x) = 0 Combine like terms: 1x + -3x = -2x (-3 + -2x + x2)(-3 + -2i + x)(-3 + 2i + x) = 0 Multiply (-3 + -2x + x2) * (-3 + -2i + x) (-3(-3 + -2i + x) + -2x * (-3 + -2i + x) + x2(-3 + -2i + x))(-3 + 2i + x) = 0 ((-3 * -3 + -2i * -3 + x * -3) + -2x * (-3 + -2i + x) + x2(-3 + -2i + x))(-3 + 2i + x) = 0 ((9 + 6i + -3x) + -2x * (-3 + -2i + x) + x2(-3 + -2i + x))(-3 + 2i + x) = 0 (9 + 6i + -3x + (-3 * -2x + -2i * -2x + x * -2x) + x2(-3 + -2i + x))(-3 + 2i + x) = 0 Reorder the terms: (9 + 6i + -3x + (4ix + 6x + -2x2) + x2(-3 + -2i + x))(-3 + 2i + x) = 0 (9 + 6i + -3x + (4ix + 6x + -2x2) + x2(-3 + -2i + x))(-3 + 2i + x) = 0 (9 + 6i + -3x + 4ix + 6x + -2x2 + (-3 * x2 + -2i * x2 + x * x2))(-3 + 2i + x) = 0 Reorder the terms: (9 + 6i + -3x + 4ix + 6x + -2x2 + (-2ix2 + -3x2 + x3))(-3 + 2i + x) = 0 (9 + 6i + -3x + 4ix + 6x + -2x2 + (-2ix2 + -3x2 + x3))(-3 + 2i + x) = 0 Reorder the terms: (9 + 6i + 4ix + -2ix2 + -3x + 6x + -2x2 + -3x2 + x3)(-3 + 2i + x) = 0 Combine like terms: -3x + 6x = 3x (9 + 6i + 4ix + -2ix2 + 3x + -2x2 + -3x2 + x3)(-3 + 2i + x) = 0 Combine like terms: -2x2 + -3x2 = -5x2 (9 + 6i + 4ix + -2ix2 + 3x + -5x2 + x3)(-3 + 2i + x) = 0 Multiply (9 + 6i + 4ix + -2ix2 + 3x + -5x2 + x3) * (-3 + 2i + x) (9(-3 + 2i + x) + 6i * (-3 + 2i + x) + 4ix * (-3 + 2i + x) + -2ix2 * (-3 + 2i + x) + 3x * (-3 + 2i + x) + -5x2 * (-3 + 2i + x) + x3(-3 + 2i + x)) = 0 ((-3 * 9 + 2i * 9 + x * 9) + 6i * (-3 + 2i + x) + 4ix * (-3 + 2i + x) + -2ix2 * (-3 + 2i + x) + 3x * (-3 + 2i + x) + -5x2 * (-3 + 2i + x) + x3(-3 + 2i + x)) = 0 ((-27 + 18i + 9x) + 6i * (-3 + 2i + x) + 4ix * (-3 + 2i + x) + -2ix2 * (-3 + 2i + x) + 3x * (-3 + 2i + x) + -5x2 * (-3 + 2i + x) + x3(-3 + 2i + x)) = 0 (-27 + 18i + 9x + (-3 * 6i + 2i * 6i + x * 6i) + 4ix * (-3 + 2i + x) + -2ix2 * (-3 + 2i + x) + 3x * (-3 + 2i + x) + -5x2 * (-3 + 2i + x) + x3(-3 + 2i + x)) = 0 Reorder the terms: (-27 + 18i + 9x + (-18i + 6ix + 12i2) + 4ix * (-3 + 2i + x) + -2ix2 * (-3 + 2i + x) + 3x * (-3 + 2i + x) + -5x2 * (-3 + 2i + x) + x3(-3 + 2i + x)) = 0 (-27 + 18i + 9x + (-18i + 6ix + 12i2) + 4ix * (-3 + 2i + x) + -2ix2 * (-3 + 2i + x) + 3x * (-3 + 2i + x) + -5x2 * (-3 + 2i + x) + x3(-3 + 2i + x)) = 0 (-27 + 18i + 9x + -18i + 6ix + 12i2 + (-3 * 4ix + 2i * 4ix + x * 4ix) + -2ix2 * (-3 + 2i + x) + 3x * (-3 + 2i + x) + -5x2 * (-3 + 2i + x) + x3(-3 + 2i + x)) = 0 Reorder the terms: (-27 + 18i + 9x + -18i + 6ix + 12i2 + (-12ix + 4ix2 + 8i2x) + -2ix2 * (-3 + 2i + x) + 3x * (-3 + 2i + x) + -5x2 * (-3 + 2i + x) + x3(-3 + 2i + x)) = 0 (-27 + 18i + 9x + -18i + 6ix + 12i2 + (-12ix + 4ix2 + 8i2x) + -2ix2 * (-3 + 2i + x) + 3x * (-3 + 2i + x) + -5x2 * (-3 + 2i + x) + x3(-3 + 2i + x)) = 0 (-27 + 18i + 9x + -18i + 6ix + 12i2 + -12ix + 4ix2 + 8i2x + (-3 * -2ix2 + 2i * -2ix2 + x * -2ix2) + 3x * (-3 + 2i + x) + -5x2 * (-3 + 2i + x) + x3(-3 + 2i + x)) = 0 Reorder the terms: (-27 + 18i + 9x + -18i + 6ix + 12i2 + -12ix + 4ix2 + 8i2x + (6ix2 + -2ix3 + -4i2x2) + 3x * (-3 + 2i + x) + -5x2 * (-3 + 2i + x) + x3(-3 + 2i + x)) = 0 (-27 + 18i + 9x + -18i + 6ix + 12i2 + -12ix + 4ix2 + 8i2x + (6ix2 + -2ix3 + -4i2x2) + 3x * (-3 + 2i + x) + -5x2 * (-3 + 2i + x) + x3(-3 + 2i + x)) = 0 (-27 + 18i + 9x + -18i + 6ix + 12i2 + -12ix + 4ix2 + 8i2x + 6ix2 + -2ix3 + -4i2x2 + (-3 * 3x + 2i * 3x + x * 3x) + -5x2 * (-3 + 2i + x) + x3(-3 + 2i + x)) = 0 Reorder the terms: (-27 + 18i + 9x + -18i + 6ix + 12i2 + -12ix + 4ix2 + 8i2x + 6ix2 + -2ix3 + -4i2x2 + (6ix + -9x + 3x2) + -5x2 * (-3 + 2i + x) + x3(-3 + 2i + x)) = 0 (-27 + 18i + 9x + -18i + 6ix + 12i2 + -12ix + 4ix2 + 8i2x + 6ix2 + -2ix3 + -4i2x2 + (6ix + -9x + 3x2) + -5x2 * (-3 + 2i + x) + x3(-3 + 2i + x)) = 0 (-27 + 18i + 9x + -18i + 6ix + 12i2 + -12ix + 4ix2 + 8i2x + 6ix2 + -2ix3 + -4i2x2 + 6ix + -9x + 3x2 + (-3 * -5x2 + 2i * -5x2 + x * -5x2) + x3(-3 + 2i + x)) = 0 Reorder the terms: (-27 + 18i + 9x + -18i + 6ix + 12i2 + -12ix + 4ix2 + 8i2x + 6ix2 + -2ix3 + -4i2x2 + 6ix + -9x + 3x2 + (-10ix2 + 15x2 + -5x3) + x3(-3 + 2i + x)) = 0 (-27 + 18i + 9x + -18i + 6ix + 12i2 + -12ix + 4ix2 + 8i2x + 6ix2 + -2ix3 + -4i2x2 + 6ix + -9x + 3x2 + (-10ix2 + 15x2 + -5x3) + x3(-3 + 2i + x)) = 0 (-27 + 18i + 9x + -18i + 6ix + 12i2 + -12ix + 4ix2 + 8i2x + 6ix2 + -2ix3 + -4i2x2 + 6ix + -9x + 3x2 + -10ix2 + 15x2 + -5x3 + (-3 * x3 + 2i * x3 + x * x3)) = 0 Reorder the terms: (-27 + 18i + 9x + -18i + 6ix + 12i2 + -12ix + 4ix2 + 8i2x + 6ix2 + -2ix3 + -4i2x2 + 6ix + -9x + 3x2 + -10ix2 + 15x2 + -5x3 + (2ix3 + -3x3 + x4)) = 0 (-27 + 18i + 9x + -18i + 6ix + 12i2 + -12ix + 4ix2 + 8i2x + 6ix2 + -2ix3 + -4i2x2 + 6ix + -9x + 3x2 + -10ix2 + 15x2 + -5x3 + (2ix3 + -3x3 + x4)) = 0 Reorder the terms: (-27 + 18i + -18i + 6ix + -12ix + 6ix + 4ix2 + 6ix2 + -10ix2 + -2ix3 + 2ix3 + 12i2 + 8i2x + -4i2x2 + 9x + -9x + 3x2 + 15x2 + -5x3 + -3x3 + x4) = 0 Combine like terms: 18i + -18i = 0 (-27 + 0 + 6ix + -12ix + 6ix + 4ix2 + 6ix2 + -10ix2 + -2ix3 + 2ix3 + 12i2 + 8i2x + -4i2x2 + 9x + -9x + 3x2 + 15x2 + -5x3 + -3x3 + x4) = 0 (-27 + 6ix + -12ix + 6ix + 4ix2 + 6ix2 + -10ix2 + -2ix3 + 2ix3 + 12i2 + 8i2x + -4i2x2 + 9x + -9x + 3x2 + 15x2 + -5x3 + -3x3 + x4) = 0 Combine like terms: 6ix + -12ix = -6ix (-27 + -6ix + 6ix + 4ix2 + 6ix2 + -10ix2 + -2ix3 + 2ix3 + 12i2 + 8i2x + -4i2x2 + 9x + -9x + 3x2 + 15x2 + -5x3 + -3x3 + x4) = 0 Combine like terms: -6ix + 6ix = 0 (-27 + 0 + 4ix2 + 6ix2 + -10ix2 + -2ix3 + 2ix3 + 12i2 + 8i2x + -4i2x2 + 9x + -9x + 3x2 + 15x2 + -5x3 + -3x3 + x4) = 0 (-27 + 4ix2 + 6ix2 + -10ix2 + -2ix3 + 2ix3 + 12i2 + 8i2x + -4i2x2 + 9x + -9x + 3x2 + 15x2 + -5x3 + -3x3 + x4) = 0 Combine like terms: 4ix2 + 6ix2 = 10ix2 (-27 + 10ix2 + -10ix2 + -2ix3 + 2ix3 + 12i2 + 8i2x + -4i2x2 + 9x + -9x + 3x2 + 15x2 + -5x3 + -3x3 + x4) = 0 Combine like terms: 10ix2 + -10ix2 = 0 (-27 + 0 + -2ix3 + 2ix3 + 12i2 + 8i2x + -4i2x2 + 9x + -9x + 3x2 + 15x2 + -5x3 + -3x3 + x4) = 0 (-27 + -2ix3 + 2ix3 + 12i2 + 8i2x + -4i2x2 + 9x + -9x + 3x2 + 15x2 + -5x3 + -3x3 + x4) = 0 Combine like terms: -2ix3 + 2ix3 = 0 (-27 + 0 + 12i2 + 8i2x + -4i2x2 + 9x + -9x + 3x2 + 15x2 + -5x3 + -3x3 + x4) = 0 (-27 + 12i2 + 8i2x + -4i2x2 + 9x + -9x + 3x2 + 15x2 + -5x3 + -3x3 + x4) = 0 Combine like terms: 9x + -9x = 0 (-27 + 12i2 + 8i2x + -4i2x2 + 0 + 3x2 + 15x2 + -5x3 + -3x3 + x4) = 0 (-27 + 12i2 + 8i2x + -4i2x2 + 3x2 + 15x2 + -5x3 + -3x3 + x4) = 0 Combine like terms: 3x2 + 15x2 = 18x2 (-27 + 12i2 + 8i2x + -4i2x2 + 18x2 + -5x3 + -3x3 + x4) = 0 Combine like terms: -5x3 + -3x3 = -8x3 (-27 + 12i2 + 8i2x + -4i2x2 + 18x2 + -8x3 + x4) = 0 Solving -27 + 12i2 + 8i2x + -4i2x2 + 18x2 + -8x3 + x4 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '27' to each side of the equation. -27 + 12i2 + 8i2x + -4i2x2 + 18x2 + -8x3 + 27 + x4 = 0 + 27 Reorder the terms: -27 + 27 + 12i2 + 8i2x + -4i2x2 + 18x2 + -8x3 + x4 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + 12i2 + 8i2x + -4i2x2 + 18x2 + -8x3 + x4 = 0 + 27 12i2 + 8i2x + -4i2x2 + 18x2 + -8x3 + x4 = 0 + 27 Combine like terms: 0 + 27 = 27 12i2 + 8i2x + -4i2x2 + 18x2 + -8x3 + x4 = 27 Add '-18x2' to each side of the equation. 12i2 + 8i2x + -4i2x2 + 18x2 + -8x3 + -18x2 + x4 = 27 + -18x2 Reorder the terms: 12i2 + 8i2x + -4i2x2 + 18x2 + -18x2 + -8x3 + x4 = 27 + -18x2 Combine like terms: 18x2 + -18x2 = 0 12i2 + 8i2x + -4i2x2 + 0 + -8x3 + x4 = 27 + -18x2 12i2 + 8i2x + -4i2x2 + -8x3 + x4 = 27 + -18x2 Add '8x3' to each side of the equation. 12i2 + 8i2x + -4i2x2 + -8x3 + 8x3 + x4 = 27 + -18x2 + 8x3 Combine like terms: -8x3 + 8x3 = 0 12i2 + 8i2x + -4i2x2 + 0 + x4 = 27 + -18x2 + 8x3 12i2 + 8i2x + -4i2x2 + x4 = 27 + -18x2 + 8x3 Add '-1x4' to each side of the equation. 12i2 + 8i2x + -4i2x2 + x4 + -1x4 = 27 + -18x2 + 8x3 + -1x4 Combine like terms: x4 + -1x4 = 0 12i2 + 8i2x + -4i2x2 + 0 = 27 + -18x2 + 8x3 + -1x4 12i2 + 8i2x + -4i2x2 = 27 + -18x2 + 8x3 + -1x4 Reorder the terms: -27 + 12i2 + 8i2x + -4i2x2 + 18x2 + -8x3 + x4 = 27 + -18x2 + 8x3 + -1x4 + -27 + 18x2 + -8x3 + x4 Reorder the terms: -27 + 12i2 + 8i2x + -4i2x2 + 18x2 + -8x3 + x4 = 27 + -27 + -18x2 + 18x2 + 8x3 + -8x3 + -1x4 + x4 Combine like terms: 27 + -27 = 0 -27 + 12i2 + 8i2x + -4i2x2 + 18x2 + -8x3 + x4 = 0 + -18x2 + 18x2 + 8x3 + -8x3 + -1x4 + x4 -27 + 12i2 + 8i2x + -4i2x2 + 18x2 + -8x3 + x4 = -18x2 + 18x2 + 8x3 + -8x3 + -1x4 + x4 Combine like terms: -18x2 + 18x2 = 0 -27 + 12i2 + 8i2x + -4i2x2 + 18x2 + -8x3 + x4 = 0 + 8x3 + -8x3 + -1x4 + x4 -27 + 12i2 + 8i2x + -4i2x2 + 18x2 + -8x3 + x4 = 8x3 + -8x3 + -1x4 + x4 Combine like terms: 8x3 + -8x3 = 0 -27 + 12i2 + 8i2x + -4i2x2 + 18x2 + -8x3 + x4 = 0 + -1x4 + x4 -27 + 12i2 + 8i2x + -4i2x2 + 18x2 + -8x3 + x4 = -1x4 + x4 Combine like terms: -1x4 + x4 = 0 -27 + 12i2 + 8i2x + -4i2x2 + 18x2 + -8x3 + x4 = 0 The solution to this equation could not be determined.
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