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Simplifying (x + -4)(x + -2 + i)(x + -2 + -1i) = 0 Reorder the terms: (-4 + x)(x + -2 + i)(x + -2 + -1i) = 0 Reorder the terms: (-4 + x)(-2 + i + x)(x + -2 + -1i) = 0 Reorder the terms: (-4 + x)(-2 + i + x)(-2 + -1i + x) = 0 Multiply (-4 + x) * (-2 + i + x) (-4(-2 + i + x) + x(-2 + i + x))(-2 + -1i + x) = 0 ((-2 * -4 + i * -4 + x * -4) + x(-2 + i + x))(-2 + -1i + x) = 0 ((8 + -4i + -4x) + x(-2 + i + x))(-2 + -1i + x) = 0 (8 + -4i + -4x + (-2 * x + i * x + x * x))(-2 + -1i + x) = 0 Reorder the terms: (8 + -4i + -4x + (ix + -2x + x2))(-2 + -1i + x) = 0 (8 + -4i + -4x + (ix + -2x + x2))(-2 + -1i + x) = 0 Reorder the terms: (8 + -4i + ix + -4x + -2x + x2)(-2 + -1i + x) = 0 Combine like terms: -4x + -2x = -6x (8 + -4i + ix + -6x + x2)(-2 + -1i + x) = 0 Multiply (8 + -4i + ix + -6x + x2) * (-2 + -1i + x) (8(-2 + -1i + x) + -4i * (-2 + -1i + x) + ix(-2 + -1i + x) + -6x * (-2 + -1i + x) + x2(-2 + -1i + x)) = 0 ((-2 * 8 + -1i * 8 + x * 8) + -4i * (-2 + -1i + x) + ix(-2 + -1i + x) + -6x * (-2 + -1i + x) + x2(-2 + -1i + x)) = 0 ((-16 + -8i + 8x) + -4i * (-2 + -1i + x) + ix(-2 + -1i + x) + -6x * (-2 + -1i + x) + x2(-2 + -1i + x)) = 0 (-16 + -8i + 8x + (-2 * -4i + -1i * -4i + x * -4i) + ix(-2 + -1i + x) + -6x * (-2 + -1i + x) + x2(-2 + -1i + x)) = 0 Reorder the terms: (-16 + -8i + 8x + (8i + -4ix + 4i2) + ix(-2 + -1i + x) + -6x * (-2 + -1i + x) + x2(-2 + -1i + x)) = 0 (-16 + -8i + 8x + (8i + -4ix + 4i2) + ix(-2 + -1i + x) + -6x * (-2 + -1i + x) + x2(-2 + -1i + x)) = 0 (-16 + -8i + 8x + 8i + -4ix + 4i2 + (-2 * ix + -1i * ix + x * ix) + -6x * (-2 + -1i + x) + x2(-2 + -1i + x)) = 0 Reorder the terms: (-16 + -8i + 8x + 8i + -4ix + 4i2 + (-2ix + ix2 + -1i2x) + -6x * (-2 + -1i + x) + x2(-2 + -1i + x)) = 0 (-16 + -8i + 8x + 8i + -4ix + 4i2 + (-2ix + ix2 + -1i2x) + -6x * (-2 + -1i + x) + x2(-2 + -1i + x)) = 0 (-16 + -8i + 8x + 8i + -4ix + 4i2 + -2ix + ix2 + -1i2x + (-2 * -6x + -1i * -6x + x * -6x) + x2(-2 + -1i + x)) = 0 Reorder the terms: (-16 + -8i + 8x + 8i + -4ix + 4i2 + -2ix + ix2 + -1i2x + (6ix + 12x + -6x2) + x2(-2 + -1i + x)) = 0 (-16 + -8i + 8x + 8i + -4ix + 4i2 + -2ix + ix2 + -1i2x + (6ix + 12x + -6x2) + x2(-2 + -1i + x)) = 0 (-16 + -8i + 8x + 8i + -4ix + 4i2 + -2ix + ix2 + -1i2x + 6ix + 12x + -6x2 + (-2 * x2 + -1i * x2 + x * x2)) = 0 Reorder the terms: (-16 + -8i + 8x + 8i + -4ix + 4i2 + -2ix + ix2 + -1i2x + 6ix + 12x + -6x2 + (-1ix2 + -2x2 + x3)) = 0 (-16 + -8i + 8x + 8i + -4ix + 4i2 + -2ix + ix2 + -1i2x + 6ix + 12x + -6x2 + (-1ix2 + -2x2 + x3)) = 0 Reorder the terms: (-16 + -8i + 8i + -4ix + -2ix + 6ix + ix2 + -1ix2 + 4i2 + -1i2x + 8x + 12x + -6x2 + -2x2 + x3) = 0 Combine like terms: -8i + 8i = 0 (-16 + 0 + -4ix + -2ix + 6ix + ix2 + -1ix2 + 4i2 + -1i2x + 8x + 12x + -6x2 + -2x2 + x3) = 0 (-16 + -4ix + -2ix + 6ix + ix2 + -1ix2 + 4i2 + -1i2x + 8x + 12x + -6x2 + -2x2 + x3) = 0 Combine like terms: -4ix + -2ix = -6ix (-16 + -6ix + 6ix + ix2 + -1ix2 + 4i2 + -1i2x + 8x + 12x + -6x2 + -2x2 + x3) = 0 Combine like terms: -6ix + 6ix = 0 (-16 + 0 + ix2 + -1ix2 + 4i2 + -1i2x + 8x + 12x + -6x2 + -2x2 + x3) = 0 (-16 + ix2 + -1ix2 + 4i2 + -1i2x + 8x + 12x + -6x2 + -2x2 + x3) = 0 Combine like terms: ix2 + -1ix2 = 0 (-16 + 0 + 4i2 + -1i2x + 8x + 12x + -6x2 + -2x2 + x3) = 0 (-16 + 4i2 + -1i2x + 8x + 12x + -6x2 + -2x2 + x3) = 0 Combine like terms: 8x + 12x = 20x (-16 + 4i2 + -1i2x + 20x + -6x2 + -2x2 + x3) = 0 Combine like terms: -6x2 + -2x2 = -8x2 (-16 + 4i2 + -1i2x + 20x + -8x2 + x3) = 0 Solving -16 + 4i2 + -1i2x + 20x + -8x2 + x3 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 4i2 + -1i2x + 20x + -8x2 + 16 + x3 = 0 + 16 Reorder the terms: -16 + 16 + 4i2 + -1i2x + 20x + -8x2 + x3 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 4i2 + -1i2x + 20x + -8x2 + x3 = 0 + 16 4i2 + -1i2x + 20x + -8x2 + x3 = 0 + 16 Combine like terms: 0 + 16 = 16 4i2 + -1i2x + 20x + -8x2 + x3 = 16 Add '-20x' to each side of the equation. 4i2 + -1i2x + 20x + -8x2 + -20x + x3 = 16 + -20x Reorder the terms: 4i2 + -1i2x + 20x + -20x + -8x2 + x3 = 16 + -20x Combine like terms: 20x + -20x = 0 4i2 + -1i2x + 0 + -8x2 + x3 = 16 + -20x 4i2 + -1i2x + -8x2 + x3 = 16 + -20x Add '8x2' to each side of the equation. 4i2 + -1i2x + -8x2 + 8x2 + x3 = 16 + -20x + 8x2 Combine like terms: -8x2 + 8x2 = 0 4i2 + -1i2x + 0 + x3 = 16 + -20x + 8x2 4i2 + -1i2x + x3 = 16 + -20x + 8x2 Add '-1x3' to each side of the equation. 4i2 + -1i2x + x3 + -1x3 = 16 + -20x + 8x2 + -1x3 Combine like terms: x3 + -1x3 = 0 4i2 + -1i2x + 0 = 16 + -20x + 8x2 + -1x3 4i2 + -1i2x = 16 + -20x + 8x2 + -1x3 Reorder the terms: -16 + 4i2 + -1i2x + 20x + -8x2 + x3 = 16 + -20x + 8x2 + -1x3 + -16 + 20x + -8x2 + x3 Reorder the terms: -16 + 4i2 + -1i2x + 20x + -8x2 + x3 = 16 + -16 + -20x + 20x + 8x2 + -8x2 + -1x3 + x3 Combine like terms: 16 + -16 = 0 -16 + 4i2 + -1i2x + 20x + -8x2 + x3 = 0 + -20x + 20x + 8x2 + -8x2 + -1x3 + x3 -16 + 4i2 + -1i2x + 20x + -8x2 + x3 = -20x + 20x + 8x2 + -8x2 + -1x3 + x3 Combine like terms: -20x + 20x = 0 -16 + 4i2 + -1i2x + 20x + -8x2 + x3 = 0 + 8x2 + -8x2 + -1x3 + x3 -16 + 4i2 + -1i2x + 20x + -8x2 + x3 = 8x2 + -8x2 + -1x3 + x3 Combine like terms: 8x2 + -8x2 = 0 -16 + 4i2 + -1i2x + 20x + -8x2 + x3 = 0 + -1x3 + x3 -16 + 4i2 + -1i2x + 20x + -8x2 + x3 = -1x3 + x3 Combine like terms: -1x3 + x3 = 0 -16 + 4i2 + -1i2x + 20x + -8x2 + x3 = 0 The solution to this equation could not be determined.
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