(x-4)(x-(2-5i))(x-(2+5i))=0

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Solution for (x-4)(x-(2-5i))(x-(2+5i))=0 equation: 


Simplifying
(x + -4)(x + -1(2 + -5i))(x + -1(2 + 5i)) = 0

Reorder the terms:
(-4 + x)(x + -1(2 + -5i))(x + -1(2 + 5i)) = 0
(-4 + x)(x + (2 * -1 + -5i * -1))(x + -1(2 + 5i)) = 0
(-4 + x)(x + (-2 + 5i))(x + -1(2 + 5i)) = 0

Reorder the terms:
(-4 + x)(-2 + 5i + x)(x + -1(2 + 5i)) = 0
(-4 + x)(-2 + 5i + x)(x + (2 * -1 + 5i * -1)) = 0
(-4 + x)(-2 + 5i + x)(x + (-2 + -5i)) = 0

Reorder the terms:
(-4 + x)(-2 + 5i + x)(-2 + -5i + x) = 0

Multiply (-4 + x) * (-2 + 5i + x)
(-4(-2 + 5i + x) + x(-2 + 5i + x))(-2 + -5i + x) = 0
((-2 * -4 + 5i * -4 + x * -4) + x(-2 + 5i + x))(-2 + -5i + x) = 0
((8 + -20i + -4x) + x(-2 + 5i + x))(-2 + -5i + x) = 0
(8 + -20i + -4x + (-2 * x + 5i * x + x * x))(-2 + -5i + x) = 0

Reorder the terms:
(8 + -20i + -4x + (5ix + -2x + x2))(-2 + -5i + x) = 0
(8 + -20i + -4x + (5ix + -2x + x2))(-2 + -5i + x) = 0

Reorder the terms:
(8 + -20i + 5ix + -4x + -2x + x2)(-2 + -5i + x) = 0

Combine like terms: -4x + -2x = -6x
(8 + -20i + 5ix + -6x + x2)(-2 + -5i + x) = 0

Multiply (8 + -20i + 5ix + -6x + x2) * (-2 + -5i + x)
(8(-2 + -5i + x) + -20i * (-2 + -5i + x) + 5ix * (-2 + -5i + x) + -6x * (-2 + -5i + x) + x2(-2 + -5i + x)) = 0
((-2 * 8 + -5i * 8 + x * 8) + -20i * (-2 + -5i + x) + 5ix * (-2 + -5i + x) + -6x * (-2 + -5i + x) + x2(-2 + -5i + x)) = 0
((-16 + -40i + 8x) + -20i * (-2 + -5i + x) + 5ix * (-2 + -5i + x) + -6x * (-2 + -5i + x) + x2(-2 + -5i + x)) = 0
(-16 + -40i + 8x + (-2 * -20i + -5i * -20i + x * -20i) + 5ix * (-2 + -5i + x) + -6x * (-2 + -5i + x) + x2(-2 + -5i + x)) = 0

Reorder the terms:
(-16 + -40i + 8x + (40i + -20ix + 100i2) + 5ix * (-2 + -5i + x) + -6x * (-2 + -5i + x) + x2(-2 + -5i + x)) = 0
(-16 + -40i + 8x + (40i + -20ix + 100i2) + 5ix * (-2 + -5i + x) + -6x * (-2 + -5i + x) + x2(-2 + -5i + x)) = 0
(-16 + -40i + 8x + 40i + -20ix + 100i2 + (-2 * 5ix + -5i * 5ix + x * 5ix) + -6x * (-2 + -5i + x) + x2(-2 + -5i + x)) = 0

Reorder the terms:
(-16 + -40i + 8x + 40i + -20ix + 100i2 + (-10ix + 5ix2 + -25i2x) + -6x * (-2 + -5i + x) + x2(-2 + -5i + x)) = 0
(-16 + -40i + 8x + 40i + -20ix + 100i2 + (-10ix + 5ix2 + -25i2x) + -6x * (-2 + -5i + x) + x2(-2 + -5i + x)) = 0
(-16 + -40i + 8x + 40i + -20ix + 100i2 + -10ix + 5ix2 + -25i2x + (-2 * -6x + -5i * -6x + x * -6x) + x2(-2 + -5i + x)) = 0

Reorder the terms:
(-16 + -40i + 8x + 40i + -20ix + 100i2 + -10ix + 5ix2 + -25i2x + (30ix + 12x + -6x2) + x2(-2 + -5i + x)) = 0
(-16 + -40i + 8x + 40i + -20ix + 100i2 + -10ix + 5ix2 + -25i2x + (30ix + 12x + -6x2) + x2(-2 + -5i + x)) = 0
(-16 + -40i + 8x + 40i + -20ix + 100i2 + -10ix + 5ix2 + -25i2x + 30ix + 12x + -6x2 + (-2 * x2 + -5i * x2 + x * x2)) = 0

Reorder the terms:
(-16 + -40i + 8x + 40i + -20ix + 100i2 + -10ix + 5ix2 + -25i2x + 30ix + 12x + -6x2 + (-5ix2 + -2x2 + x3)) = 0
(-16 + -40i + 8x + 40i + -20ix + 100i2 + -10ix + 5ix2 + -25i2x + 30ix + 12x + -6x2 + (-5ix2 + -2x2 + x3)) = 0

Reorder the terms:
(-16 + -40i + 40i + -20ix + -10ix + 30ix + 5ix2 + -5ix2 + 100i2 + -25i2x + 8x + 12x + -6x2 + -2x2 + x3) = 0

Combine like terms: -40i + 40i = 0
(-16 + 0 + -20ix + -10ix + 30ix + 5ix2 + -5ix2 + 100i2 + -25i2x + 8x + 12x + -6x2 + -2x2 + x3) = 0
(-16 + -20ix + -10ix + 30ix + 5ix2 + -5ix2 + 100i2 + -25i2x + 8x + 12x + -6x2 + -2x2 + x3) = 0

Combine like terms: -20ix + -10ix = -30ix
(-16 + -30ix + 30ix + 5ix2 + -5ix2 + 100i2 + -25i2x + 8x + 12x + -6x2 + -2x2 + x3) = 0

Combine like terms: -30ix + 30ix = 0
(-16 + 0 + 5ix2 + -5ix2 + 100i2 + -25i2x + 8x + 12x + -6x2 + -2x2 + x3) = 0
(-16 + 5ix2 + -5ix2 + 100i2 + -25i2x + 8x + 12x + -6x2 + -2x2 + x3) = 0

Combine like terms: 5ix2 + -5ix2 = 0
(-16 + 0 + 100i2 + -25i2x + 8x + 12x + -6x2 + -2x2 + x3) = 0
(-16 + 100i2 + -25i2x + 8x + 12x + -6x2 + -2x2 + x3) = 0

Combine like terms: 8x + 12x = 20x
(-16 + 100i2 + -25i2x + 20x + -6x2 + -2x2 + x3) = 0

Combine like terms: -6x2 + -2x2 = -8x2
(-16 + 100i2 + -25i2x + 20x + -8x2 + x3) = 0

Solving
-16 + 100i2 + -25i2x + 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 + 100i2 + -25i2x + 20x + -8x2 + 16 + x3 = 0 + 16

Reorder the terms:
-16 + 16 + 100i2 + -25i2x + 20x + -8x2 + x3 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + 100i2 + -25i2x + 20x + -8x2 + x3 = 0 + 16
100i2 + -25i2x + 20x + -8x2 + x3 = 0 + 16

Combine like terms: 0 + 16 = 16
100i2 + -25i2x + 20x + -8x2 + x3 = 16

Add '-20x' to each side of the equation.
100i2 + -25i2x + 20x + -8x2 + -20x + x3 = 16 + -20x

Reorder the terms:
100i2 + -25i2x + 20x + -20x + -8x2 + x3 = 16 + -20x

Combine like terms: 20x + -20x = 0
100i2 + -25i2x + 0 + -8x2 + x3 = 16 + -20x
100i2 + -25i2x + -8x2 + x3 = 16 + -20x

Add '8x2' to each side of the equation.
100i2 + -25i2x + -8x2 + 8x2 + x3 = 16 + -20x + 8x2

Combine like terms: -8x2 + 8x2 = 0
100i2 + -25i2x + 0 + x3 = 16 + -20x + 8x2
100i2 + -25i2x + x3 = 16 + -20x + 8x2

Add '-1x3' to each side of the equation.
100i2 + -25i2x + x3 + -1x3 = 16 + -20x + 8x2 + -1x3

Combine like terms: x3 + -1x3 = 0
100i2 + -25i2x + 0 = 16 + -20x + 8x2 + -1x3
100i2 + -25i2x = 16 + -20x + 8x2 + -1x3

Reorder the terms:
-16 + 100i2 + -25i2x + 20x + -8x2 + x3 = 16 + -20x + 8x2 + -1x3 + -16 + 20x + -8x2 + x3

Reorder the terms:
-16 + 100i2 + -25i2x + 20x + -8x2 + x3 = 16 + -16 + -20x + 20x + 8x2 + -8x2 + -1x3 + x3

Combine like terms: 16 + -16 = 0
-16 + 100i2 + -25i2x + 20x + -8x2 + x3 = 0 + -20x + 20x + 8x2 + -8x2 + -1x3 + x3
-16 + 100i2 + -25i2x + 20x + -8x2 + x3 = -20x + 20x + 8x2 + -8x2 + -1x3 + x3

Combine like terms: -20x + 20x = 0
-16 + 100i2 + -25i2x + 20x + -8x2 + x3 = 0 + 8x2 + -8x2 + -1x3 + x3
-16 + 100i2 + -25i2x + 20x + -8x2 + x3 = 8x2 + -8x2 + -1x3 + x3

Combine like terms: 8x2 + -8x2 = 0
-16 + 100i2 + -25i2x + 20x + -8x2 + x3 = 0 + -1x3 + x3
-16 + 100i2 + -25i2x + 20x + -8x2 + x3 = -1x3 + x3

Combine like terms: -1x3 + x3 = 0
-16 + 100i2 + -25i2x + 20x + -8x2 + x3 = 0

The solution to this equation could not be determined.

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