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