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

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Solution for (X+1)(x+1)(x+2i)(x-2i)=0 equation: 


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

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

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

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

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

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

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

Multiply (1 + 1X + 1x + xX) * (2i + x)
(1(2i + x) + 1X * (2i + x) + 1x * (2i + x) + xX(2i + x))(-2i + x) = 0
((2i * 1 + x * 1) + 1X * (2i + x) + 1x * (2i + x) + xX(2i + x))(-2i + x) = 0
((2i + 1x) + 1X * (2i + x) + 1x * (2i + x) + xX(2i + x))(-2i + x) = 0
(2i + 1x + (2i * 1X + x * 1X) + 1x * (2i + x) + xX(2i + x))(-2i + x) = 0
(2i + 1x + (2iX + 1xX) + 1x * (2i + x) + xX(2i + x))(-2i + x) = 0
(2i + 1x + 2iX + 1xX + (2i * 1x + x * 1x) + xX(2i + x))(-2i + x) = 0
(2i + 1x + 2iX + 1xX + (2ix + 1x2) + xX(2i + x))(-2i + x) = 0
(2i + 1x + 2iX + 1xX + 2ix + 1x2 + (2i * xX + x * xX))(-2i + x) = 0
(2i + 1x + 2iX + 1xX + 2ix + 1x2 + (2ixX + x2X))(-2i + x) = 0

Reorder the terms:
(2i + 2iX + 2ix + 2ixX + 1x + 1xX + 1x2 + x2X)(-2i + x) = 0
(2i + 2iX + 2ix + 2ixX + 1x + 1xX + 1x2 + x2X)(-2i + x) = 0

Multiply (2i + 2iX + 2ix + 2ixX + 1x + 1xX + 1x2 + x2X) * (-2i + x)
(2i * (-2i + x) + 2iX * (-2i + x) + 2ix * (-2i + x) + 2ixX * (-2i + x) + 1x * (-2i + x) + 1xX * (-2i + x) + 1x2 * (-2i + x) + x2X(-2i + x)) = 0
((-2i * 2i + x * 2i) + 2iX * (-2i + x) + 2ix * (-2i + x) + 2ixX * (-2i + x) + 1x * (-2i + x) + 1xX * (-2i + x) + 1x2 * (-2i + x) + x2X(-2i + x)) = 0

Reorder the terms:
((2ix + -4i2) + 2iX * (-2i + x) + 2ix * (-2i + x) + 2ixX * (-2i + x) + 1x * (-2i + x) + 1xX * (-2i + x) + 1x2 * (-2i + x) + x2X(-2i + x)) = 0
((2ix + -4i2) + 2iX * (-2i + x) + 2ix * (-2i + x) + 2ixX * (-2i + x) + 1x * (-2i + x) + 1xX * (-2i + x) + 1x2 * (-2i + x) + x2X(-2i + x)) = 0
(2ix + -4i2 + (-2i * 2iX + x * 2iX) + 2ix * (-2i + x) + 2ixX * (-2i + x) + 1x * (-2i + x) + 1xX * (-2i + x) + 1x2 * (-2i + x) + x2X(-2i + x)) = 0

Reorder the terms:
(2ix + -4i2 + (2ixX + -4i2X) + 2ix * (-2i + x) + 2ixX * (-2i + x) + 1x * (-2i + x) + 1xX * (-2i + x) + 1x2 * (-2i + x) + x2X(-2i + x)) = 0
(2ix + -4i2 + (2ixX + -4i2X) + 2ix * (-2i + x) + 2ixX * (-2i + x) + 1x * (-2i + x) + 1xX * (-2i + x) + 1x2 * (-2i + x) + x2X(-2i + x)) = 0
(2ix + -4i2 + 2ixX + -4i2X + (-2i * 2ix + x * 2ix) + 2ixX * (-2i + x) + 1x * (-2i + x) + 1xX * (-2i + x) + 1x2 * (-2i + x) + x2X(-2i + x)) = 0

Reorder the terms:
(2ix + -4i2 + 2ixX + -4i2X + (2ix2 + -4i2x) + 2ixX * (-2i + x) + 1x * (-2i + x) + 1xX * (-2i + x) + 1x2 * (-2i + x) + x2X(-2i + x)) = 0
(2ix + -4i2 + 2ixX + -4i2X + (2ix2 + -4i2x) + 2ixX * (-2i + x) + 1x * (-2i + x) + 1xX * (-2i + x) + 1x2 * (-2i + x) + x2X(-2i + x)) = 0
(2ix + -4i2 + 2ixX + -4i2X + 2ix2 + -4i2x + (-2i * 2ixX + x * 2ixX) + 1x * (-2i + x) + 1xX * (-2i + x) + 1x2 * (-2i + x) + x2X(-2i + x)) = 0

Reorder the terms:
(2ix + -4i2 + 2ixX + -4i2X + 2ix2 + -4i2x + (2ix2X + -4i2xX) + 1x * (-2i + x) + 1xX * (-2i + x) + 1x2 * (-2i + x) + x2X(-2i + x)) = 0
(2ix + -4i2 + 2ixX + -4i2X + 2ix2 + -4i2x + (2ix2X + -4i2xX) + 1x * (-2i + x) + 1xX * (-2i + x) + 1x2 * (-2i + x) + x2X(-2i + x)) = 0
(2ix + -4i2 + 2ixX + -4i2X + 2ix2 + -4i2x + 2ix2X + -4i2xX + (-2i * 1x + x * 1x) + 1xX * (-2i + x) + 1x2 * (-2i + x) + x2X(-2i + x)) = 0
(2ix + -4i2 + 2ixX + -4i2X + 2ix2 + -4i2x + 2ix2X + -4i2xX + (-2ix + 1x2) + 1xX * (-2i + x) + 1x2 * (-2i + x) + x2X(-2i + x)) = 0
(2ix + -4i2 + 2ixX + -4i2X + 2ix2 + -4i2x + 2ix2X + -4i2xX + -2ix + 1x2 + (-2i * 1xX + x * 1xX) + 1x2 * (-2i + x) + x2X(-2i + x)) = 0
(2ix + -4i2 + 2ixX + -4i2X + 2ix2 + -4i2x + 2ix2X + -4i2xX + -2ix + 1x2 + (-2ixX + 1x2X) + 1x2 * (-2i + x) + x2X(-2i + x)) = 0
(2ix + -4i2 + 2ixX + -4i2X + 2ix2 + -4i2x + 2ix2X + -4i2xX + -2ix + 1x2 + -2ixX + 1x2X + (-2i * 1x2 + x * 1x2) + x2X(-2i + x)) = 0
(2ix + -4i2 + 2ixX + -4i2X + 2ix2 + -4i2x + 2ix2X + -4i2xX + -2ix + 1x2 + -2ixX + 1x2X + (-2ix2 + 1x3) + x2X(-2i + x)) = 0
(2ix + -4i2 + 2ixX + -4i2X + 2ix2 + -4i2x + 2ix2X + -4i2xX + -2ix + 1x2 + -2ixX + 1x2X + -2ix2 + 1x3 + (-2i * x2X + x * x2X)) = 0
(2ix + -4i2 + 2ixX + -4i2X + 2ix2 + -4i2x + 2ix2X + -4i2xX + -2ix + 1x2 + -2ixX + 1x2X + -2ix2 + 1x3 + (-2ix2X + x3X)) = 0

Reorder the terms:
(2ix + -2ix + 2ixX + -2ixX + 2ix2 + -2ix2 + 2ix2X + -2ix2X + -4i2 + -4i2X + -4i2x + -4i2xX + 1x2 + 1x2X + 1x3 + x3X) = 0

Combine like terms: 2ix + -2ix = 0
(0 + 2ixX + -2ixX + 2ix2 + -2ix2 + 2ix2X + -2ix2X + -4i2 + -4i2X + -4i2x + -4i2xX + 1x2 + 1x2X + 1x3 + x3X) = 0
(2ixX + -2ixX + 2ix2 + -2ix2 + 2ix2X + -2ix2X + -4i2 + -4i2X + -4i2x + -4i2xX + 1x2 + 1x2X + 1x3 + x3X) = 0

Combine like terms: 2ixX + -2ixX = 0
(0 + 2ix2 + -2ix2 + 2ix2X + -2ix2X + -4i2 + -4i2X + -4i2x + -4i2xX + 1x2 + 1x2X + 1x3 + x3X) = 0
(2ix2 + -2ix2 + 2ix2X + -2ix2X + -4i2 + -4i2X + -4i2x + -4i2xX + 1x2 + 1x2X + 1x3 + x3X) = 0

Combine like terms: 2ix2 + -2ix2 = 0
(0 + 2ix2X + -2ix2X + -4i2 + -4i2X + -4i2x + -4i2xX + 1x2 + 1x2X + 1x3 + x3X) = 0
(2ix2X + -2ix2X + -4i2 + -4i2X + -4i2x + -4i2xX + 1x2 + 1x2X + 1x3 + x3X) = 0

Combine like terms: 2ix2X + -2ix2X = 0
(0 + -4i2 + -4i2X + -4i2x + -4i2xX + 1x2 + 1x2X + 1x3 + x3X) = 0
(-4i2 + -4i2X + -4i2x + -4i2xX + 1x2 + 1x2X + 1x3 + x3X) = 0

Solving
-4i2 + -4i2X + -4i2x + -4i2xX + 1x2 + 1x2X + 1x3 + x3X = 0

Solving for variable 'i'.

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

Add '-1x2' to each side of the equation.
-4i2 + -4i2X + -4i2x + -4i2xX + 1x2 + 1x2X + 1x3 + -1x2 + x3X = 0 + -1x2

Reorder the terms:
-4i2 + -4i2X + -4i2x + -4i2xX + 1x2 + -1x2 + 1x2X + 1x3 + x3X = 0 + -1x2

Combine like terms: 1x2 + -1x2 = 0
-4i2 + -4i2X + -4i2x + -4i2xX + 0 + 1x2X + 1x3 + x3X = 0 + -1x2
-4i2 + -4i2X + -4i2x + -4i2xX + 1x2X + 1x3 + x3X = 0 + -1x2
Remove the zero:
-4i2 + -4i2X + -4i2x + -4i2xX + 1x2X + 1x3 + x3X = -1x2

Add '-1x2X' to each side of the equation.
-4i2 + -4i2X + -4i2x + -4i2xX + 1x2X + 1x3 + -1x2X + x3X = -1x2 + -1x2X

Reorder the terms:
-4i2 + -4i2X + -4i2x + -4i2xX + 1x2X + -1x2X + 1x3 + x3X = -1x2 + -1x2X

Combine like terms: 1x2X + -1x2X = 0
-4i2 + -4i2X + -4i2x + -4i2xX + 0 + 1x3 + x3X = -1x2 + -1x2X
-4i2 + -4i2X + -4i2x + -4i2xX + 1x3 + x3X = -1x2 + -1x2X

Add '-1x3' to each side of the equation.
-4i2 + -4i2X + -4i2x + -4i2xX + 1x3 + -1x3 + x3X = -1x2 + -1x2X + -1x3

Combine like terms: 1x3 + -1x3 = 0
-4i2 + -4i2X + -4i2x + -4i2xX + 0 + x3X = -1x2 + -1x2X + -1x3
-4i2 + -4i2X + -4i2x + -4i2xX + x3X = -1x2 + -1x2X + -1x3

Add '-1x3X' to each side of the equation.
-4i2 + -4i2X + -4i2x + -4i2xX + x3X + -1x3X = -1x2 + -1x2X + -1x3 + -1x3X

Combine like terms: x3X + -1x3X = 0
-4i2 + -4i2X + -4i2x + -4i2xX + 0 = -1x2 + -1x2X + -1x3 + -1x3X
-4i2 + -4i2X + -4i2x + -4i2xX = -1x2 + -1x2X + -1x3 + -1x3X

Reorder the terms:
-4i2 + -4i2X + -4i2x + -4i2xX + x2 + x2X + x3 + x3X = -1x2 + x2 + -1x2X + x2X + -1x3 + x3 + -1x3X + x3X

Combine like terms: -1x2 + x2 = 0
-4i2 + -4i2X + -4i2x + -4i2xX + x2 + x2X + x3 + x3X = 0 + -1x2X + x2X + -1x3 + x3 + -1x3X + x3X
-4i2 + -4i2X + -4i2x + -4i2xX + x2 + x2X + x3 + x3X = -1x2X + x2X + -1x3 + x3 + -1x3X + x3X

Combine like terms: -1x2X + x2X = 0
-4i2 + -4i2X + -4i2x + -4i2xX + x2 + x2X + x3 + x3X = 0 + -1x3 + x3 + -1x3X + x3X
-4i2 + -4i2X + -4i2x + -4i2xX + x2 + x2X + x3 + x3X = -1x3 + x3 + -1x3X + x3X

Combine like terms: -1x3 + x3 = 0
-4i2 + -4i2X + -4i2x + -4i2xX + x2 + x2X + x3 + x3X = 0 + -1x3X + x3X
-4i2 + -4i2X + -4i2x + -4i2xX + x2 + x2X + x3 + x3X = -1x3X + x3X

Combine like terms: -1x3X + x3X = 0
-4i2 + -4i2X + -4i2x + -4i2xX + x2 + x2X + x3 + x3X = 0

The solution to this equation could not be determined.

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