(x-1)(x+2)(x-2i)(x+2i)(x+1)=

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Solution for (x-1)(x+2)(x-2i)(x+2i)(x+1)= equation: 


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

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

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

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

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

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

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

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

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

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

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

Reorder the terms:
((4ix + 8i2) + -2ix * (2i + x) + -2ix2 * (2i + x) + -2x * (2i + x) + 1x2 * (2i + x) + x3(2i + x))(1 + x) = 0
((4ix + 8i2) + -2ix * (2i + x) + -2ix2 * (2i + x) + -2x * (2i + x) + 1x2 * (2i + x) + x3(2i + x))(1 + x) = 0
(4ix + 8i2 + (2i * -2ix + x * -2ix) + -2ix2 * (2i + x) + -2x * (2i + x) + 1x2 * (2i + x) + x3(2i + x))(1 + x) = 0

Reorder the terms:
(4ix + 8i2 + (-2ix2 + -4i2x) + -2ix2 * (2i + x) + -2x * (2i + x) + 1x2 * (2i + x) + x3(2i + x))(1 + x) = 0
(4ix + 8i2 + (-2ix2 + -4i2x) + -2ix2 * (2i + x) + -2x * (2i + x) + 1x2 * (2i + x) + x3(2i + x))(1 + x) = 0
(4ix + 8i2 + -2ix2 + -4i2x + (2i * -2ix2 + x * -2ix2) + -2x * (2i + x) + 1x2 * (2i + x) + x3(2i + x))(1 + x) = 0

Reorder the terms:
(4ix + 8i2 + -2ix2 + -4i2x + (-2ix3 + -4i2x2) + -2x * (2i + x) + 1x2 * (2i + x) + x3(2i + x))(1 + x) = 0
(4ix + 8i2 + -2ix2 + -4i2x + (-2ix3 + -4i2x2) + -2x * (2i + x) + 1x2 * (2i + x) + x3(2i + x))(1 + x) = 0
(4ix + 8i2 + -2ix2 + -4i2x + -2ix3 + -4i2x2 + (2i * -2x + x * -2x) + 1x2 * (2i + x) + x3(2i + x))(1 + x) = 0
(4ix + 8i2 + -2ix2 + -4i2x + -2ix3 + -4i2x2 + (-4ix + -2x2) + 1x2 * (2i + x) + x3(2i + x))(1 + x) = 0
(4ix + 8i2 + -2ix2 + -4i2x + -2ix3 + -4i2x2 + -4ix + -2x2 + (2i * 1x2 + x * 1x2) + x3(2i + x))(1 + x) = 0
(4ix + 8i2 + -2ix2 + -4i2x + -2ix3 + -4i2x2 + -4ix + -2x2 + (2ix2 + 1x3) + x3(2i + x))(1 + x) = 0
(4ix + 8i2 + -2ix2 + -4i2x + -2ix3 + -4i2x2 + -4ix + -2x2 + 2ix2 + 1x3 + (2i * x3 + x * x3))(1 + x) = 0
(4ix + 8i2 + -2ix2 + -4i2x + -2ix3 + -4i2x2 + -4ix + -2x2 + 2ix2 + 1x3 + (2ix3 + x4))(1 + x) = 0

Reorder the terms:
(4ix + -4ix + -2ix2 + 2ix2 + -2ix3 + 2ix3 + 8i2 + -4i2x + -4i2x2 + -2x2 + 1x3 + x4)(1 + x) = 0

Combine like terms: 4ix + -4ix = 0
(0 + -2ix2 + 2ix2 + -2ix3 + 2ix3 + 8i2 + -4i2x + -4i2x2 + -2x2 + 1x3 + x4)(1 + x) = 0
(-2ix2 + 2ix2 + -2ix3 + 2ix3 + 8i2 + -4i2x + -4i2x2 + -2x2 + 1x3 + x4)(1 + x) = 0

Combine like terms: -2ix2 + 2ix2 = 0
(0 + -2ix3 + 2ix3 + 8i2 + -4i2x + -4i2x2 + -2x2 + 1x3 + x4)(1 + x) = 0
(-2ix3 + 2ix3 + 8i2 + -4i2x + -4i2x2 + -2x2 + 1x3 + x4)(1 + x) = 0

Combine like terms: -2ix3 + 2ix3 = 0
(0 + 8i2 + -4i2x + -4i2x2 + -2x2 + 1x3 + x4)(1 + x) = 0
(8i2 + -4i2x + -4i2x2 + -2x2 + 1x3 + x4)(1 + x) = 0

Multiply (8i2 + -4i2x + -4i2x2 + -2x2 + 1x3 + x4) * (1 + x)
(8i2 * (1 + x) + -4i2x * (1 + x) + -4i2x2 * (1 + x) + -2x2 * (1 + x) + 1x3 * (1 + x) + x4(1 + x)) = 0
((1 * 8i2 + x * 8i2) + -4i2x * (1 + x) + -4i2x2 * (1 + x) + -2x2 * (1 + x) + 1x3 * (1 + x) + x4(1 + x)) = 0
((8i2 + 8i2x) + -4i2x * (1 + x) + -4i2x2 * (1 + x) + -2x2 * (1 + x) + 1x3 * (1 + x) + x4(1 + x)) = 0
(8i2 + 8i2x + (1 * -4i2x + x * -4i2x) + -4i2x2 * (1 + x) + -2x2 * (1 + x) + 1x3 * (1 + x) + x4(1 + x)) = 0
(8i2 + 8i2x + (-4i2x + -4i2x2) + -4i2x2 * (1 + x) + -2x2 * (1 + x) + 1x3 * (1 + x) + x4(1 + x)) = 0
(8i2 + 8i2x + -4i2x + -4i2x2 + (1 * -4i2x2 + x * -4i2x2) + -2x2 * (1 + x) + 1x3 * (1 + x) + x4(1 + x)) = 0
(8i2 + 8i2x + -4i2x + -4i2x2 + (-4i2x2 + -4i2x3) + -2x2 * (1 + x) + 1x3 * (1 + x) + x4(1 + x)) = 0
(8i2 + 8i2x + -4i2x + -4i2x2 + -4i2x2 + -4i2x3 + (1 * -2x2 + x * -2x2) + 1x3 * (1 + x) + x4(1 + x)) = 0
(8i2 + 8i2x + -4i2x + -4i2x2 + -4i2x2 + -4i2x3 + (-2x2 + -2x3) + 1x3 * (1 + x) + x4(1 + x)) = 0
(8i2 + 8i2x + -4i2x + -4i2x2 + -4i2x2 + -4i2x3 + -2x2 + -2x3 + (1 * 1x3 + x * 1x3) + x4(1 + x)) = 0
(8i2 + 8i2x + -4i2x + -4i2x2 + -4i2x2 + -4i2x3 + -2x2 + -2x3 + (1x3 + 1x4) + x4(1 + x)) = 0
(8i2 + 8i2x + -4i2x + -4i2x2 + -4i2x2 + -4i2x3 + -2x2 + -2x3 + 1x3 + 1x4 + (1 * x4 + x * x4)) = 0
(8i2 + 8i2x + -4i2x + -4i2x2 + -4i2x2 + -4i2x3 + -2x2 + -2x3 + 1x3 + 1x4 + (1x4 + x5)) = 0

Combine like terms: 8i2x + -4i2x = 4i2x
(8i2 + 4i2x + -4i2x2 + -4i2x2 + -4i2x3 + -2x2 + -2x3 + 1x3 + 1x4 + 1x4 + x5) = 0

Combine like terms: -4i2x2 + -4i2x2 = -8i2x2
(8i2 + 4i2x + -8i2x2 + -4i2x3 + -2x2 + -2x3 + 1x3 + 1x4 + 1x4 + x5) = 0

Combine like terms: -2x3 + 1x3 = -1x3
(8i2 + 4i2x + -8i2x2 + -4i2x3 + -2x2 + -1x3 + 1x4 + 1x4 + x5) = 0

Combine like terms: 1x4 + 1x4 = 2x4
(8i2 + 4i2x + -8i2x2 + -4i2x3 + -2x2 + -1x3 + 2x4 + x5) = 0

Solving
8i2 + 4i2x + -8i2x2 + -4i2x3 + -2x2 + -1x3 + 2x4 + x5 = 0

Solving for variable 'i'.

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

Add '2x2' to each side of the equation.
8i2 + 4i2x + -8i2x2 + -4i2x3 + -2x2 + -1x3 + 2x4 + 2x2 + x5 = 0 + 2x2

Reorder the terms:
8i2 + 4i2x + -8i2x2 + -4i2x3 + -2x2 + 2x2 + -1x3 + 2x4 + x5 = 0 + 2x2

Combine like terms: -2x2 + 2x2 = 0
8i2 + 4i2x + -8i2x2 + -4i2x3 + 0 + -1x3 + 2x4 + x5 = 0 + 2x2
8i2 + 4i2x + -8i2x2 + -4i2x3 + -1x3 + 2x4 + x5 = 0 + 2x2
Remove the zero:
8i2 + 4i2x + -8i2x2 + -4i2x3 + -1x3 + 2x4 + x5 = 2x2

Add 'x3' to each side of the equation.
8i2 + 4i2x + -8i2x2 + -4i2x3 + -1x3 + 2x4 + x3 + x5 = 2x2 + x3

Reorder the terms:
8i2 + 4i2x + -8i2x2 + -4i2x3 + -1x3 + x3 + 2x4 + x5 = 2x2 + x3

Combine like terms: -1x3 + x3 = 0
8i2 + 4i2x + -8i2x2 + -4i2x3 + 0 + 2x4 + x5 = 2x2 + x3
8i2 + 4i2x + -8i2x2 + -4i2x3 + 2x4 + x5 = 2x2 + x3

Add '-2x4' to each side of the equation.
8i2 + 4i2x + -8i2x2 + -4i2x3 + 2x4 + -2x4 + x5 = 2x2 + x3 + -2x4

Combine like terms: 2x4 + -2x4 = 0
8i2 + 4i2x + -8i2x2 + -4i2x3 + 0 + x5 = 2x2 + x3 + -2x4
8i2 + 4i2x + -8i2x2 + -4i2x3 + x5 = 2x2 + x3 + -2x4

Add '-1x5' to each side of the equation.
8i2 + 4i2x + -8i2x2 + -4i2x3 + x5 + -1x5 = 2x2 + x3 + -2x4 + -1x5

Combine like terms: x5 + -1x5 = 0
8i2 + 4i2x + -8i2x2 + -4i2x3 + 0 = 2x2 + x3 + -2x4 + -1x5
8i2 + 4i2x + -8i2x2 + -4i2x3 = 2x2 + x3 + -2x4 + -1x5

Reorder the terms:
8i2 + 4i2x + -8i2x2 + -4i2x3 + -2x2 + -1x3 + 2x4 + x5 = 2x2 + -2x2 + x3 + -1x3 + -2x4 + 2x4 + -1x5 + x5

Combine like terms: 2x2 + -2x2 = 0
8i2 + 4i2x + -8i2x2 + -4i2x3 + -2x2 + -1x3 + 2x4 + x5 = 0 + x3 + -1x3 + -2x4 + 2x4 + -1x5 + x5
8i2 + 4i2x + -8i2x2 + -4i2x3 + -2x2 + -1x3 + 2x4 + x5 = x3 + -1x3 + -2x4 + 2x4 + -1x5 + x5

Combine like terms: x3 + -1x3 = 0
8i2 + 4i2x + -8i2x2 + -4i2x3 + -2x2 + -1x3 + 2x4 + x5 = 0 + -2x4 + 2x4 + -1x5 + x5
8i2 + 4i2x + -8i2x2 + -4i2x3 + -2x2 + -1x3 + 2x4 + x5 = -2x4 + 2x4 + -1x5 + x5

Combine like terms: -2x4 + 2x4 = 0
8i2 + 4i2x + -8i2x2 + -4i2x3 + -2x2 + -1x3 + 2x4 + x5 = 0 + -1x5 + x5
8i2 + 4i2x + -8i2x2 + -4i2x3 + -2x2 + -1x3 + 2x4 + x5 = -1x5 + x5

Combine like terms: -1x5 + x5 = 0
8i2 + 4i2x + -8i2x2 + -4i2x3 + -2x2 + -1x3 + 2x4 + x5 = 0

The solution to this equation could not be determined.

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