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

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


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

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

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

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

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

Combine like terms: -2x + -3x = -5x
(6 + -5x + x2)(-2 + 2i + x) = 0

Multiply (6 + -5x + x2) * (-2 + 2i + x)
(6(-2 + 2i + x) + -5x * (-2 + 2i + x) + x2(-2 + 2i + x)) = 0
((-2 * 6 + 2i * 6 + x * 6) + -5x * (-2 + 2i + x) + x2(-2 + 2i + x)) = 0
((-12 + 12i + 6x) + -5x * (-2 + 2i + x) + x2(-2 + 2i + x)) = 0
(-12 + 12i + 6x + (-2 * -5x + 2i * -5x + x * -5x) + x2(-2 + 2i + x)) = 0

Reorder the terms:
(-12 + 12i + 6x + (-10ix + 10x + -5x2) + x2(-2 + 2i + x)) = 0
(-12 + 12i + 6x + (-10ix + 10x + -5x2) + x2(-2 + 2i + x)) = 0
(-12 + 12i + 6x + -10ix + 10x + -5x2 + (-2 * x2 + 2i * x2 + x * x2)) = 0

Reorder the terms:
(-12 + 12i + 6x + -10ix + 10x + -5x2 + (2ix2 + -2x2 + x3)) = 0
(-12 + 12i + 6x + -10ix + 10x + -5x2 + (2ix2 + -2x2 + x3)) = 0

Reorder the terms:
(-12 + 12i + -10ix + 2ix2 + 6x + 10x + -5x2 + -2x2 + x3) = 0

Combine like terms: 6x + 10x = 16x
(-12 + 12i + -10ix + 2ix2 + 16x + -5x2 + -2x2 + x3) = 0

Combine like terms: -5x2 + -2x2 = -7x2
(-12 + 12i + -10ix + 2ix2 + 16x + -7x2 + x3) = 0

Solving
-12 + 12i + -10ix + 2ix2 + 16x + -7x2 + x3 = 0

Solving for variable 'i'.

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

Add '12' to each side of the equation.
-12 + 12i + -10ix + 2ix2 + 16x + -7x2 + 12 + x3 = 0 + 12

Reorder the terms:
-12 + 12 + 12i + -10ix + 2ix2 + 16x + -7x2 + x3 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + 12i + -10ix + 2ix2 + 16x + -7x2 + x3 = 0 + 12
12i + -10ix + 2ix2 + 16x + -7x2 + x3 = 0 + 12

Combine like terms: 0 + 12 = 12
12i + -10ix + 2ix2 + 16x + -7x2 + x3 = 12

Add '-16x' to each side of the equation.
12i + -10ix + 2ix2 + 16x + -7x2 + -16x + x3 = 12 + -16x

Reorder the terms:
12i + -10ix + 2ix2 + 16x + -16x + -7x2 + x3 = 12 + -16x

Combine like terms: 16x + -16x = 0
12i + -10ix + 2ix2 + 0 + -7x2 + x3 = 12 + -16x
12i + -10ix + 2ix2 + -7x2 + x3 = 12 + -16x

Add '7x2' to each side of the equation.
12i + -10ix + 2ix2 + -7x2 + 7x2 + x3 = 12 + -16x + 7x2

Combine like terms: -7x2 + 7x2 = 0
12i + -10ix + 2ix2 + 0 + x3 = 12 + -16x + 7x2
12i + -10ix + 2ix2 + x3 = 12 + -16x + 7x2

Add '-1x3' to each side of the equation.
12i + -10ix + 2ix2 + x3 + -1x3 = 12 + -16x + 7x2 + -1x3

Combine like terms: x3 + -1x3 = 0
12i + -10ix + 2ix2 + 0 = 12 + -16x + 7x2 + -1x3
12i + -10ix + 2ix2 = 12 + -16x + 7x2 + -1x3

Reorder the terms:
-12 + 12i + -10ix + 2ix2 + 16x + -7x2 + x3 = 12 + -16x + 7x2 + -1x3 + -12 + 16x + -7x2 + x3

Reorder the terms:
-12 + 12i + -10ix + 2ix2 + 16x + -7x2 + x3 = 12 + -12 + -16x + 16x + 7x2 + -7x2 + -1x3 + x3

Combine like terms: 12 + -12 = 0
-12 + 12i + -10ix + 2ix2 + 16x + -7x2 + x3 = 0 + -16x + 16x + 7x2 + -7x2 + -1x3 + x3
-12 + 12i + -10ix + 2ix2 + 16x + -7x2 + x3 = -16x + 16x + 7x2 + -7x2 + -1x3 + x3

Combine like terms: -16x + 16x = 0
-12 + 12i + -10ix + 2ix2 + 16x + -7x2 + x3 = 0 + 7x2 + -7x2 + -1x3 + x3
-12 + 12i + -10ix + 2ix2 + 16x + -7x2 + x3 = 7x2 + -7x2 + -1x3 + x3

Combine like terms: 7x2 + -7x2 = 0
-12 + 12i + -10ix + 2ix2 + 16x + -7x2 + x3 = 0 + -1x3 + x3
-12 + 12i + -10ix + 2ix2 + 16x + -7x2 + x3 = -1x3 + x3

Combine like terms: -1x3 + x3 = 0
-12 + 12i + -10ix + 2ix2 + 16x + -7x2 + x3 = 0

The solution to this equation could not be determined.

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