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

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Solution for (x-2)*(x+4)*(x-(1+3i))=0 equation: 


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

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

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

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

Multiply (-2 + x) * (4 + x)
(-2(4 + x) + x(4 + x))(-1 + -3i + x) = 0
((4 * -2 + x * -2) + x(4 + x))(-1 + -3i + x) = 0
((-8 + -2x) + x(4 + x))(-1 + -3i + x) = 0
(-8 + -2x + (4 * x + x * x))(-1 + -3i + x) = 0
(-8 + -2x + (4x + x2))(-1 + -3i + x) = 0

Combine like terms: -2x + 4x = 2x
(-8 + 2x + x2)(-1 + -3i + x) = 0

Multiply (-8 + 2x + x2) * (-1 + -3i + x)
(-8(-1 + -3i + x) + 2x * (-1 + -3i + x) + x2(-1 + -3i + x)) = 0
((-1 * -8 + -3i * -8 + x * -8) + 2x * (-1 + -3i + x) + x2(-1 + -3i + x)) = 0
((8 + 24i + -8x) + 2x * (-1 + -3i + x) + x2(-1 + -3i + x)) = 0
(8 + 24i + -8x + (-1 * 2x + -3i * 2x + x * 2x) + x2(-1 + -3i + x)) = 0

Reorder the terms:
(8 + 24i + -8x + (-6ix + -2x + 2x2) + x2(-1 + -3i + x)) = 0
(8 + 24i + -8x + (-6ix + -2x + 2x2) + x2(-1 + -3i + x)) = 0
(8 + 24i + -8x + -6ix + -2x + 2x2 + (-1 * x2 + -3i * x2 + x * x2)) = 0

Reorder the terms:
(8 + 24i + -8x + -6ix + -2x + 2x2 + (-3ix2 + -1x2 + x3)) = 0
(8 + 24i + -8x + -6ix + -2x + 2x2 + (-3ix2 + -1x2 + x3)) = 0

Reorder the terms:
(8 + 24i + -6ix + -3ix2 + -8x + -2x + 2x2 + -1x2 + x3) = 0

Combine like terms: -8x + -2x = -10x
(8 + 24i + -6ix + -3ix2 + -10x + 2x2 + -1x2 + x3) = 0

Combine like terms: 2x2 + -1x2 = 1x2
(8 + 24i + -6ix + -3ix2 + -10x + 1x2 + x3) = 0

Solving
8 + 24i + -6ix + -3ix2 + -10x + 1x2 + x3 = 0

Solving for variable 'i'.

Move all terms containing i to the left, all other terms to the right.

Add '-8' to each side of the equation.
8 + 24i + -6ix + -3ix2 + -10x + 1x2 + -8 + x3 = 0 + -8

Reorder the terms:
8 + -8 + 24i + -6ix + -3ix2 + -10x + 1x2 + x3 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 24i + -6ix + -3ix2 + -10x + 1x2 + x3 = 0 + -8
24i + -6ix + -3ix2 + -10x + 1x2 + x3 = 0 + -8

Combine like terms: 0 + -8 = -8
24i + -6ix + -3ix2 + -10x + 1x2 + x3 = -8

Add '10x' to each side of the equation.
24i + -6ix + -3ix2 + -10x + 1x2 + 10x + x3 = -8 + 10x

Reorder the terms:
24i + -6ix + -3ix2 + -10x + 10x + 1x2 + x3 = -8 + 10x

Combine like terms: -10x + 10x = 0
24i + -6ix + -3ix2 + 0 + 1x2 + x3 = -8 + 10x
24i + -6ix + -3ix2 + 1x2 + x3 = -8 + 10x

Add '-1x2' to each side of the equation.
24i + -6ix + -3ix2 + 1x2 + -1x2 + x3 = -8 + 10x + -1x2

Combine like terms: 1x2 + -1x2 = 0
24i + -6ix + -3ix2 + 0 + x3 = -8 + 10x + -1x2
24i + -6ix + -3ix2 + x3 = -8 + 10x + -1x2

Add '-1x3' to each side of the equation.
24i + -6ix + -3ix2 + x3 + -1x3 = -8 + 10x + -1x2 + -1x3

Combine like terms: x3 + -1x3 = 0
24i + -6ix + -3ix2 + 0 = -8 + 10x + -1x2 + -1x3
24i + -6ix + -3ix2 = -8 + 10x + -1x2 + -1x3

Reorder the terms:
8 + 24i + -6ix + -3ix2 + -10x + x2 + x3 = -8 + 10x + -1x2 + -1x3 + 8 + -10x + x2 + x3

Reorder the terms:
8 + 24i + -6ix + -3ix2 + -10x + x2 + x3 = -8 + 8 + 10x + -10x + -1x2 + x2 + -1x3 + x3

Combine like terms: -8 + 8 = 0
8 + 24i + -6ix + -3ix2 + -10x + x2 + x3 = 0 + 10x + -10x + -1x2 + x2 + -1x3 + x3
8 + 24i + -6ix + -3ix2 + -10x + x2 + x3 = 10x + -10x + -1x2 + x2 + -1x3 + x3

Combine like terms: 10x + -10x = 0
8 + 24i + -6ix + -3ix2 + -10x + x2 + x3 = 0 + -1x2 + x2 + -1x3 + x3
8 + 24i + -6ix + -3ix2 + -10x + x2 + x3 = -1x2 + x2 + -1x3 + x3

Combine like terms: -1x2 + x2 = 0
8 + 24i + -6ix + -3ix2 + -10x + x2 + x3 = 0 + -1x3 + x3
8 + 24i + -6ix + -3ix2 + -10x + x2 + x3 = -1x3 + x3

Combine like terms: -1x3 + x3 = 0
8 + 24i + -6ix + -3ix2 + -10x + x2 + x3 = 0

The solution to this equation could not be determined.

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