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