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Simplifying (x + 4)(x + -1 + 2i)(x + -1 + -2i) = 0 Reorder the terms: (4 + x)(x + -1 + 2i)(x + -1 + -2i) = 0 Reorder the terms: (4 + x)(-1 + 2i + x)(x + -1 + -2i) = 0 Reorder the terms: (4 + x)(-1 + 2i + x)(-1 + -2i + x) = 0 Multiply (4 + x) * (-1 + 2i + x) (4(-1 + 2i + x) + x(-1 + 2i + x))(-1 + -2i + x) = 0 ((-1 * 4 + 2i * 4 + x * 4) + x(-1 + 2i + x))(-1 + -2i + x) = 0 ((-4 + 8i + 4x) + x(-1 + 2i + x))(-1 + -2i + x) = 0 (-4 + 8i + 4x + (-1 * x + 2i * x + x * x))(-1 + -2i + x) = 0 Reorder the terms: (-4 + 8i + 4x + (2ix + -1x + x2))(-1 + -2i + x) = 0 (-4 + 8i + 4x + (2ix + -1x + x2))(-1 + -2i + x) = 0 Reorder the terms: (-4 + 8i + 2ix + 4x + -1x + x2)(-1 + -2i + x) = 0 Combine like terms: 4x + -1x = 3x (-4 + 8i + 2ix + 3x + x2)(-1 + -2i + x) = 0 Multiply (-4 + 8i + 2ix + 3x + x2) * (-1 + -2i + x) (-4(-1 + -2i + x) + 8i * (-1 + -2i + x) + 2ix * (-1 + -2i + x) + 3x * (-1 + -2i + x) + x2(-1 + -2i + x)) = 0 ((-1 * -4 + -2i * -4 + x * -4) + 8i * (-1 + -2i + x) + 2ix * (-1 + -2i + x) + 3x * (-1 + -2i + x) + x2(-1 + -2i + x)) = 0 ((4 + 8i + -4x) + 8i * (-1 + -2i + x) + 2ix * (-1 + -2i + x) + 3x * (-1 + -2i + x) + x2(-1 + -2i + x)) = 0 (4 + 8i + -4x + (-1 * 8i + -2i * 8i + x * 8i) + 2ix * (-1 + -2i + x) + 3x * (-1 + -2i + x) + x2(-1 + -2i + x)) = 0 Reorder the terms: (4 + 8i + -4x + (-8i + 8ix + -16i2) + 2ix * (-1 + -2i + x) + 3x * (-1 + -2i + x) + x2(-1 + -2i + x)) = 0 (4 + 8i + -4x + (-8i + 8ix + -16i2) + 2ix * (-1 + -2i + x) + 3x * (-1 + -2i + x) + x2(-1 + -2i + x)) = 0 (4 + 8i + -4x + -8i + 8ix + -16i2 + (-1 * 2ix + -2i * 2ix + x * 2ix) + 3x * (-1 + -2i + x) + x2(-1 + -2i + x)) = 0 Reorder the terms: (4 + 8i + -4x + -8i + 8ix + -16i2 + (-2ix + 2ix2 + -4i2x) + 3x * (-1 + -2i + x) + x2(-1 + -2i + x)) = 0 (4 + 8i + -4x + -8i + 8ix + -16i2 + (-2ix + 2ix2 + -4i2x) + 3x * (-1 + -2i + x) + x2(-1 + -2i + x)) = 0 (4 + 8i + -4x + -8i + 8ix + -16i2 + -2ix + 2ix2 + -4i2x + (-1 * 3x + -2i * 3x + x * 3x) + x2(-1 + -2i + x)) = 0 Reorder the terms: (4 + 8i + -4x + -8i + 8ix + -16i2 + -2ix + 2ix2 + -4i2x + (-6ix + -3x + 3x2) + x2(-1 + -2i + x)) = 0 (4 + 8i + -4x + -8i + 8ix + -16i2 + -2ix + 2ix2 + -4i2x + (-6ix + -3x + 3x2) + x2(-1 + -2i + x)) = 0 (4 + 8i + -4x + -8i + 8ix + -16i2 + -2ix + 2ix2 + -4i2x + -6ix + -3x + 3x2 + (-1 * x2 + -2i * x2 + x * x2)) = 0 Reorder the terms: (4 + 8i + -4x + -8i + 8ix + -16i2 + -2ix + 2ix2 + -4i2x + -6ix + -3x + 3x2 + (-2ix2 + -1x2 + x3)) = 0 (4 + 8i + -4x + -8i + 8ix + -16i2 + -2ix + 2ix2 + -4i2x + -6ix + -3x + 3x2 + (-2ix2 + -1x2 + x3)) = 0 Reorder the terms: (4 + 8i + -8i + 8ix + -2ix + -6ix + 2ix2 + -2ix2 + -16i2 + -4i2x + -4x + -3x + 3x2 + -1x2 + x3) = 0 Combine like terms: 8i + -8i = 0 (4 + 0 + 8ix + -2ix + -6ix + 2ix2 + -2ix2 + -16i2 + -4i2x + -4x + -3x + 3x2 + -1x2 + x3) = 0 (4 + 8ix + -2ix + -6ix + 2ix2 + -2ix2 + -16i2 + -4i2x + -4x + -3x + 3x2 + -1x2 + x3) = 0 Combine like terms: 8ix + -2ix = 6ix (4 + 6ix + -6ix + 2ix2 + -2ix2 + -16i2 + -4i2x + -4x + -3x + 3x2 + -1x2 + x3) = 0 Combine like terms: 6ix + -6ix = 0 (4 + 0 + 2ix2 + -2ix2 + -16i2 + -4i2x + -4x + -3x + 3x2 + -1x2 + x3) = 0 (4 + 2ix2 + -2ix2 + -16i2 + -4i2x + -4x + -3x + 3x2 + -1x2 + x3) = 0 Combine like terms: 2ix2 + -2ix2 = 0 (4 + 0 + -16i2 + -4i2x + -4x + -3x + 3x2 + -1x2 + x3) = 0 (4 + -16i2 + -4i2x + -4x + -3x + 3x2 + -1x2 + x3) = 0 Combine like terms: -4x + -3x = -7x (4 + -16i2 + -4i2x + -7x + 3x2 + -1x2 + x3) = 0 Combine like terms: 3x2 + -1x2 = 2x2 (4 + -16i2 + -4i2x + -7x + 2x2 + x3) = 0 Solving 4 + -16i2 + -4i2x + -7x + 2x2 + x3 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -16i2 + -4i2x + -7x + 2x2 + -4 + x3 = 0 + -4 Reorder the terms: 4 + -4 + -16i2 + -4i2x + -7x + 2x2 + x3 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -16i2 + -4i2x + -7x + 2x2 + x3 = 0 + -4 -16i2 + -4i2x + -7x + 2x2 + x3 = 0 + -4 Combine like terms: 0 + -4 = -4 -16i2 + -4i2x + -7x + 2x2 + x3 = -4 Add '7x' to each side of the equation. -16i2 + -4i2x + -7x + 2x2 + 7x + x3 = -4 + 7x Reorder the terms: -16i2 + -4i2x + -7x + 7x + 2x2 + x3 = -4 + 7x Combine like terms: -7x + 7x = 0 -16i2 + -4i2x + 0 + 2x2 + x3 = -4 + 7x -16i2 + -4i2x + 2x2 + x3 = -4 + 7x Add '-2x2' to each side of the equation. -16i2 + -4i2x + 2x2 + -2x2 + x3 = -4 + 7x + -2x2 Combine like terms: 2x2 + -2x2 = 0 -16i2 + -4i2x + 0 + x3 = -4 + 7x + -2x2 -16i2 + -4i2x + x3 = -4 + 7x + -2x2 Add '-1x3' to each side of the equation. -16i2 + -4i2x + x3 + -1x3 = -4 + 7x + -2x2 + -1x3 Combine like terms: x3 + -1x3 = 0 -16i2 + -4i2x + 0 = -4 + 7x + -2x2 + -1x3 -16i2 + -4i2x = -4 + 7x + -2x2 + -1x3 Reorder the terms: 4 + -16i2 + -4i2x + -7x + 2x2 + x3 = -4 + 7x + -2x2 + -1x3 + 4 + -7x + 2x2 + x3 Reorder the terms: 4 + -16i2 + -4i2x + -7x + 2x2 + x3 = -4 + 4 + 7x + -7x + -2x2 + 2x2 + -1x3 + x3 Combine like terms: -4 + 4 = 0 4 + -16i2 + -4i2x + -7x + 2x2 + x3 = 0 + 7x + -7x + -2x2 + 2x2 + -1x3 + x3 4 + -16i2 + -4i2x + -7x + 2x2 + x3 = 7x + -7x + -2x2 + 2x2 + -1x3 + x3 Combine like terms: 7x + -7x = 0 4 + -16i2 + -4i2x + -7x + 2x2 + x3 = 0 + -2x2 + 2x2 + -1x3 + x3 4 + -16i2 + -4i2x + -7x + 2x2 + x3 = -2x2 + 2x2 + -1x3 + x3 Combine like terms: -2x2 + 2x2 = 0 4 + -16i2 + -4i2x + -7x + 2x2 + x3 = 0 + -1x3 + x3 4 + -16i2 + -4i2x + -7x + 2x2 + x3 = -1x3 + x3 Combine like terms: -1x3 + x3 = 0 4 + -16i2 + -4i2x + -7x + 2x2 + x3 = 0 The solution to this equation could not be determined.
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