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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 = 2x (-8 + 4i + ix + 2x + x2)(-2 + -1i + x) = 0 Multiply (-8 + 4i + ix + 2x + x2) * (-2 + -1i + x) (-8(-2 + -1i + x) + 4i * (-2 + -1i + x) + ix(-2 + -1i + x) + 2x * (-2 + -1i + x) + x2(-2 + -1i + x)) = 0 ((-2 * -8 + -1i * -8 + x * -8) + 4i * (-2 + -1i + x) + ix(-2 + -1i + x) + 2x * (-2 + -1i + x) + x2(-2 + -1i + x)) = 0 ((16 + 8i + -8x) + 4i * (-2 + -1i + x) + ix(-2 + -1i + x) + 2x * (-2 + -1i + x) + x2(-2 + -1i + x)) = 0 (16 + 8i + -8x + (-2 * 4i + -1i * 4i + x * 4i) + ix(-2 + -1i + x) + 2x * (-2 + -1i + x) + x2(-2 + -1i + x)) = 0 Reorder the terms: (16 + 8i + -8x + (-8i + 4ix + -4i2) + ix(-2 + -1i + x) + 2x * (-2 + -1i + x) + x2(-2 + -1i + x)) = 0 (16 + 8i + -8x + (-8i + 4ix + -4i2) + ix(-2 + -1i + x) + 2x * (-2 + -1i + x) + x2(-2 + -1i + x)) = 0 (16 + 8i + -8x + -8i + 4ix + -4i2 + (-2 * ix + -1i * ix + x * ix) + 2x * (-2 + -1i + x) + x2(-2 + -1i + x)) = 0 Reorder the terms: (16 + 8i + -8x + -8i + 4ix + -4i2 + (-2ix + ix2 + -1i2x) + 2x * (-2 + -1i + x) + x2(-2 + -1i + x)) = 0 (16 + 8i + -8x + -8i + 4ix + -4i2 + (-2ix + ix2 + -1i2x) + 2x * (-2 + -1i + x) + x2(-2 + -1i + x)) = 0 (16 + 8i + -8x + -8i + 4ix + -4i2 + -2ix + ix2 + -1i2x + (-2 * 2x + -1i * 2x + x * 2x) + x2(-2 + -1i + x)) = 0 Reorder the terms: (16 + 8i + -8x + -8i + 4ix + -4i2 + -2ix + ix2 + -1i2x + (-2ix + -4x + 2x2) + x2(-2 + -1i + x)) = 0 (16 + 8i + -8x + -8i + 4ix + -4i2 + -2ix + ix2 + -1i2x + (-2ix + -4x + 2x2) + x2(-2 + -1i + x)) = 0 (16 + 8i + -8x + -8i + 4ix + -4i2 + -2ix + ix2 + -1i2x + -2ix + -4x + 2x2 + (-2 * x2 + -1i * x2 + x * x2)) = 0 Reorder the terms: (16 + 8i + -8x + -8i + 4ix + -4i2 + -2ix + ix2 + -1i2x + -2ix + -4x + 2x2 + (-1ix2 + -2x2 + x3)) = 0 (16 + 8i + -8x + -8i + 4ix + -4i2 + -2ix + ix2 + -1i2x + -2ix + -4x + 2x2 + (-1ix2 + -2x2 + x3)) = 0 Reorder the terms: (16 + 8i + -8i + 4ix + -2ix + -2ix + ix2 + -1ix2 + -4i2 + -1i2x + -8x + -4x + 2x2 + -2x2 + x3) = 0 Combine like terms: 8i + -8i = 0 (16 + 0 + 4ix + -2ix + -2ix + ix2 + -1ix2 + -4i2 + -1i2x + -8x + -4x + 2x2 + -2x2 + x3) = 0 (16 + 4ix + -2ix + -2ix + ix2 + -1ix2 + -4i2 + -1i2x + -8x + -4x + 2x2 + -2x2 + x3) = 0 Combine like terms: 4ix + -2ix = 2ix (16 + 2ix + -2ix + ix2 + -1ix2 + -4i2 + -1i2x + -8x + -4x + 2x2 + -2x2 + x3) = 0 Combine like terms: 2ix + -2ix = 0 (16 + 0 + ix2 + -1ix2 + -4i2 + -1i2x + -8x + -4x + 2x2 + -2x2 + x3) = 0 (16 + ix2 + -1ix2 + -4i2 + -1i2x + -8x + -4x + 2x2 + -2x2 + x3) = 0 Combine like terms: ix2 + -1ix2 = 0 (16 + 0 + -4i2 + -1i2x + -8x + -4x + 2x2 + -2x2 + x3) = 0 (16 + -4i2 + -1i2x + -8x + -4x + 2x2 + -2x2 + x3) = 0 Combine like terms: -8x + -4x = -12x (16 + -4i2 + -1i2x + -12x + 2x2 + -2x2 + x3) = 0 Combine like terms: 2x2 + -2x2 = 0 (16 + -4i2 + -1i2x + -12x + 0 + x3) = 0 (16 + -4i2 + -1i2x + -12x + x3) = 0 Solving 16 + -4i2 + -1i2x + -12x + 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 + -12x + -16 + x3 = 0 + -16 Reorder the terms: 16 + -16 + -4i2 + -1i2x + -12x + x3 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + -4i2 + -1i2x + -12x + x3 = 0 + -16 -4i2 + -1i2x + -12x + x3 = 0 + -16 Combine like terms: 0 + -16 = -16 -4i2 + -1i2x + -12x + x3 = -16 Add '12x' to each side of the equation. -4i2 + -1i2x + -12x + 12x + x3 = -16 + 12x Combine like terms: -12x + 12x = 0 -4i2 + -1i2x + 0 + x3 = -16 + 12x -4i2 + -1i2x + x3 = -16 + 12x Add '-1x3' to each side of the equation. -4i2 + -1i2x + x3 + -1x3 = -16 + 12x + -1x3 Combine like terms: x3 + -1x3 = 0 -4i2 + -1i2x + 0 = -16 + 12x + -1x3 -4i2 + -1i2x = -16 + 12x + -1x3 Reorder the terms: 16 + -4i2 + -1i2x + -12x + x3 = -16 + 12x + -1x3 + 16 + -12x + x3 Reorder the terms: 16 + -4i2 + -1i2x + -12x + x3 = -16 + 16 + 12x + -12x + -1x3 + x3 Combine like terms: -16 + 16 = 0 16 + -4i2 + -1i2x + -12x + x3 = 0 + 12x + -12x + -1x3 + x3 16 + -4i2 + -1i2x + -12x + x3 = 12x + -12x + -1x3 + x3 Combine like terms: 12x + -12x = 0 16 + -4i2 + -1i2x + -12x + x3 = 0 + -1x3 + x3 16 + -4i2 + -1i2x + -12x + x3 = -1x3 + x3 Combine like terms: -1x3 + x3 = 0 16 + -4i2 + -1i2x + -12x + x3 = 0 The solution to this equation could not be determined.
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