(x^2-4x+2)(x+(3+i))(x-(3+i))=0

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Solution for (x^2-4x+2)(x+(3+i))(x-(3+i))=0 equation:

Simplifying
(x² + -4x + 2)(x + (3 + i))(x + -1(3 + i)) = 0

Reorder the terms:
(2 + -4x + x²)(x + (3 + i))(x + -1(3 + i)) = 0

Remove parenthesis around (3 + i)
(2 + -4x + x²)(x + 3 + i)(x + -1(3 + i)) = 0

Reorder the terms:
(2 + -4x + x²)(3 + i + x)(x + -1(3 + i)) = 0
(2 + -4x + x²)(3 + i + x)(x + (3 * -1 + i * -1)) = 0
(2 + -4x + x²)(3 + i + x)(x + (-3 + -1i)) = 0

Reorder the terms:
(2 + -4x + x²)(3 + i + x)(-3 + -1i + x) = 0

Multiply (2 + -4x + x²) * (3 + i + x)
(2(3 + i + x) + -4x * (3 + i + x) + x²(3 + i + x))(-3 + -1i + x) = 0
((3 * 2 + i * 2 + x * 2) + -4x * (3 + i + x) + x²(3 + i + x))(-3 + -1i + x) = 0
((6 + 2i + 2x) + -4x * (3 + i + x) + x²(3 + i + x))(-3 + -1i + x) = 0
(6 + 2i + 2x + (3 * -4x + i * -4x + x * -4x) + x²(3 + i + x))(-3 + -1i + x) = 0

Reorder the terms:
(6 + 2i + 2x + (-4ix + -12x + -4x²) + x²(3 + i + x))(-3 + -1i + x) = 0
(6 + 2i + 2x + (-4ix + -12x + -4x²) + x²(3 + i + x))(-3 + -1i + x) = 0
(6 + 2i + 2x + -4ix + -12x + -4x² + (3 * x² + i * x² + x * x²))(-3 + -1i + x) = 0

Reorder the terms:
(6 + 2i + 2x + -4ix + -12x + -4x² + (ix² + 3x² + x³))(-3 + -1i + x) = 0
(6 + 2i + 2x + -4ix + -12x + -4x² + (ix² + 3x² + x³))(-3 + -1i + x) = 0

Reorder the terms:
(6 + 2i + -4ix + ix² + 2x + -12x + -4x² + 3x² + x³)(-3 + -1i + x) = 0

Combine like terms: 2x + -12x = -10x
(6 + 2i + -4ix + ix² + -10x + -4x² + 3x² + x³)(-3 + -1i + x) = 0

Combine like terms: -4x² + 3x² = -1x²
(6 + 2i + -4ix + ix² + -10x + -1x² + x³)(-3 + -1i + x) = 0

Multiply (6 + 2i + -4ix + ix² + -10x + -1x² + x³) * (-3 + -1i + x)
(6(-3 + -1i + x) + 2i * (-3 + -1i + x) + -4ix * (-3 + -1i + x) + ix²(-3 + -1i + x) + -10x * (-3 + -1i + x) + -1x² * (-3 + -1i + x) + x³(-3 + -1i + x)) = 0
((-3 * 6 + -1i * 6 + x * 6) + 2i * (-3 + -1i + x) + -4ix * (-3 + -1i + x) + ix²(-3 + -1i + x) + -10x * (-3 + -1i + x) + -1x² * (-3 + -1i + x) + x³(-3 + -1i + x)) = 0
((-18 + -6i + 6x) + 2i * (-3 + -1i + x) + -4ix * (-3 + -1i + x) + ix²(-3 + -1i + x) + -10x * (-3 + -1i + x) + -1x² * (-3 + -1i + x) + x³(-3 + -1i + x)) = 0
(-18 + -6i + 6x + (-3 * 2i + -1i * 2i + x * 2i) + -4ix * (-3 + -1i + x) + ix²(-3 + -1i + x) + -10x * (-3 + -1i + x) + -1x² * (-3 + -1i + x) + x³(-3 + -1i + x)) = 0

Reorder the terms:
(-18 + -6i + 6x + (-6i + 2ix + -2i²) + -4ix * (-3 + -1i + x) + ix²(-3 + -1i + x) + -10x * (-3 + -1i + x) + -1x² * (-3 + -1i + x) + x³(-3 + -1i + x)) = 0
(-18 + -6i + 6x + (-6i + 2ix + -2i²) + -4ix * (-3 + -1i + x) + ix²(-3 + -1i + x) + -10x * (-3 + -1i + x) + -1x² * (-3 + -1i + x) + x³(-3 + -1i + x)) = 0
(-18 + -6i + 6x + -6i + 2ix + -2i² + (-3 * -4ix + -1i * -4ix + x * -4ix) + ix²(-3 + -1i + x) + -10x * (-3 + -1i + x) + -1x² * (-3 + -1i + x) + x³(-3 + -1i + x)) = 0

Reorder the terms:
(-18 + -6i + 6x + -6i + 2ix + -2i² + (12ix + -4ix² + 4i²x) + ix²(-3 + -1i + x) + -10x * (-3 + -1i + x) + -1x² * (-3 + -1i + x) + x³(-3 + -1i + x)) = 0
(-18 + -6i + 6x + -6i + 2ix + -2i² + (12ix + -4ix² + 4i²x) + ix²(-3 + -1i + x) + -10x * (-3 + -1i + x) + -1x² * (-3 + -1i + x) + x³(-3 + -1i + x)) = 0
(-18 + -6i + 6x + -6i + 2ix + -2i² + 12ix + -4ix² + 4i²x + (-3 * ix² + -1i * ix² + x * ix²) + -10x * (-3 + -1i + x) + -1x² * (-3 + -1i + x) + x³(-3 + -1i + x)) = 0

Reorder the terms:
(-18 + -6i + 6x + -6i + 2ix + -2i² + 12ix + -4ix² + 4i²x + (-3ix² + ix³ + -1i²x²) + -10x * (-3 + -1i + x) + -1x² * (-3 + -1i + x) + x³(-3 + -1i + x)) = 0
(-18 + -6i + 6x + -6i + 2ix + -2i² + 12ix + -4ix² + 4i²x + (-3ix² + ix³ + -1i²x²) + -10x * (-3 + -1i + x) + -1x² * (-3 + -1i + x) + x³(-3 + -1i + x)) = 0
(-18 + -6i + 6x + -6i + 2ix + -2i² + 12ix + -4ix² + 4i²x + -3ix² + ix³ + -1i²x² + (-3 * -10x + -1i * -10x + x * -10x) + -1x² * (-3 + -1i + x) + x³(-3 + -1i + x)) = 0

Reorder the terms:
(-18 + -6i + 6x + -6i + 2ix + -2i² + 12ix + -4ix² + 4i²x + -3ix² + ix³ + -1i²x² + (10ix + 30x + -10x²) + -1x² * (-3 + -1i + x) + x³(-3 + -1i + x)) = 0
(-18 + -6i + 6x + -6i + 2ix + -2i² + 12ix + -4ix² + 4i²x + -3ix² + ix³ + -1i²x² + (10ix + 30x + -10x²) + -1x² * (-3 + -1i + x) + x³(-3 + -1i + x)) = 0
(-18 + -6i + 6x + -6i + 2ix + -2i² + 12ix + -4ix² + 4i²x + -3ix² + ix³ + -1i²x² + 10ix + 30x + -10x² + (-3 * -1x² + -1i * -1x² + x * -1x²) + x³(-3 + -1i + x)) = 0

Reorder the terms:
(-18 + -6i + 6x + -6i + 2ix + -2i² + 12ix + -4ix² + 4i²x + -3ix² + ix³ + -1i²x² + 10ix + 30x + -10x² + (1ix² + 3x² + -1x³) + x³(-3 + -1i + x)) = 0
(-18 + -6i + 6x + -6i + 2ix + -2i² + 12ix + -4ix² + 4i²x + -3ix² + ix³ + -1i²x² + 10ix + 30x + -10x² + (1ix² + 3x² + -1x³) + x³(-3 + -1i + x)) = 0
(-18 + -6i + 6x + -6i + 2ix + -2i² + 12ix + -4ix² + 4i²x + -3ix² + ix³ + -1i²x² + 10ix + 30x + -10x² + 1ix² + 3x² + -1x³ + (-3 * x³ + -1i * x³ + x * x³)) = 0

Reorder the terms:
(-18 + -6i + 6x + -6i + 2ix + -2i² + 12ix + -4ix² + 4i²x + -3ix² + ix³ + -1i²x² + 10ix + 30x + -10x² + 1ix² + 3x² + -1x³ + (-1ix³ + -3x³ + x⁴)) = 0
(-18 + -6i + 6x + -6i + 2ix + -2i² + 12ix + -4ix² + 4i²x + -3ix² + ix³ + -1i²x² + 10ix + 30x + -10x² + 1ix² + 3x² + -1x³ + (-1ix³ + -3x³ + x⁴)) = 0

Reorder the terms:
(-18 + -6i + -6i + 2ix + 12ix + 10ix + -4ix² + -3ix² + 1ix² + ix³ + -1ix³ + -2i² + 4i²x + -1i²x² + 6x + 30x + -10x² + 3x² + -1x³ + -3x³ + x⁴) = 0

Combine like terms: -6i + -6i = -12i
(-18 + -12i + 2ix + 12ix + 10ix + -4ix² + -3ix² + 1ix² + ix³ + -1ix³ + -2i² + 4i²x + -1i²x² + 6x + 30x + -10x² + 3x² + -1x³ + -3x³ + x⁴) = 0

Combine like terms: 2ix + 12ix = 14ix
(-18 + -12i + 14ix + 10ix + -4ix² + -3ix² + 1ix² + ix³ + -1ix³ + -2i² + 4i²x + -1i²x² + 6x + 30x + -10x² + 3x² + -1x³ + -3x³ + x⁴) = 0

Combine like terms: 14ix + 10ix = 24ix
(-18 + -12i + 24ix + -4ix² + -3ix² + 1ix² + ix³ + -1ix³ + -2i² + 4i²x + -1i²x² + 6x + 30x + -10x² + 3x² + -1x³ + -3x³ + x⁴) = 0

Combine like terms: -4ix² + -3ix² = -7ix²
(-18 + -12i + 24ix + -7ix² + 1ix² + ix³ + -1ix³ + -2i² + 4i²x + -1i²x² + 6x + 30x + -10x² + 3x² + -1x³ + -3x³ + x⁴) = 0

Combine like terms: -7ix² + 1ix² = -6ix²
(-18 + -12i + 24ix + -6ix² + ix³ + -1ix³ + -2i² + 4i²x + -1i²x² + 6x + 30x + -10x² + 3x² + -1x³ + -3x³ + x⁴) = 0

Combine like terms: ix³ + -1ix³ = 0
(-18 + -12i + 24ix + -6ix² + 0 + -2i² + 4i²x + -1i²x² + 6x + 30x + -10x² + 3x² + -1x³ + -3x³ + x⁴) = 0
(-18 + -12i + 24ix + -6ix² + -2i² + 4i²x + -1i²x² + 6x + 30x + -10x² + 3x² + -1x³ + -3x³ + x⁴) = 0

Combine like terms: 6x + 30x = 36x
(-18 + -12i + 24ix + -6ix² + -2i² + 4i²x + -1i²x² + 36x + -10x² + 3x² + -1x³ + -3x³ + x⁴) = 0

Combine like terms: -10x² + 3x² = -7x²
(-18 + -12i + 24ix + -6ix² + -2i² + 4i²x + -1i²x² + 36x + -7x² + -1x³ + -3x³ + x⁴) = 0

Combine like terms: -1x³ + -3x³ = -4x³
(-18 + -12i + 24ix + -6ix² + -2i² + 4i²x + -1i²x² + 36x + -7x² + -4x³ + x⁴) = 0

Solving
-18 + -12i + 24ix + -6ix² + -2i² + 4i²x + -1i²x² + 36x + -7x² + -4x³ + x⁴ = 0

Solving for variable 'i'.

The solution to this equation could not be determined.

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(x^2-4x+2)(x+(3+i))(x-(3+i))=0

Simple and best practice solution for (x^2-4x+2)(x+(3+i))(x-(3+i))=0 equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

Solution for (x^2-4x+2)(x+(3+i))(x-(3+i))=0 equation:

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