(x-1)(X-2)(x-3i)(x+3i)=0

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


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

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

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

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

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

Multiply (-1 + x) * (-2 + X)
(-1(-2 + X) + x(-2 + X))(-3i + x)(3i + x) = 0
((-2 * -1 + X * -1) + x(-2 + X))(-3i + x)(3i + x) = 0
((2 + -1X) + x(-2 + X))(-3i + x)(3i + x) = 0
(2 + -1X + (-2 * x + X * x))(-3i + x)(3i + x) = 0
(2 + -1X + (-2x + xX))(-3i + x)(3i + x) = 0
(2 + -1X + -2x + xX)(-3i + x)(3i + x) = 0

Multiply (2 + -1X + -2x + xX) * (-3i + x)
(2(-3i + x) + -1X * (-3i + x) + -2x * (-3i + x) + xX(-3i + x))(3i + x) = 0
((-3i * 2 + x * 2) + -1X * (-3i + x) + -2x * (-3i + x) + xX(-3i + x))(3i + x) = 0
((-6i + 2x) + -1X * (-3i + x) + -2x * (-3i + x) + xX(-3i + x))(3i + x) = 0
(-6i + 2x + (-3i * -1X + x * -1X) + -2x * (-3i + x) + xX(-3i + x))(3i + x) = 0
(-6i + 2x + (3iX + -1xX) + -2x * (-3i + x) + xX(-3i + x))(3i + x) = 0
(-6i + 2x + 3iX + -1xX + (-3i * -2x + x * -2x) + xX(-3i + x))(3i + x) = 0
(-6i + 2x + 3iX + -1xX + (6ix + -2x2) + xX(-3i + x))(3i + x) = 0
(-6i + 2x + 3iX + -1xX + 6ix + -2x2 + (-3i * xX + x * xX))(3i + x) = 0
(-6i + 2x + 3iX + -1xX + 6ix + -2x2 + (-3ixX + x2X))(3i + x) = 0

Reorder the terms:
(-6i + 3iX + 6ix + -3ixX + 2x + -1xX + -2x2 + x2X)(3i + x) = 0
(-6i + 3iX + 6ix + -3ixX + 2x + -1xX + -2x2 + x2X)(3i + x) = 0

Multiply (-6i + 3iX + 6ix + -3ixX + 2x + -1xX + -2x2 + x2X) * (3i + x)
(-6i * (3i + x) + 3iX * (3i + x) + 6ix * (3i + x) + -3ixX * (3i + x) + 2x * (3i + x) + -1xX * (3i + x) + -2x2 * (3i + x) + x2X(3i + x)) = 0
((3i * -6i + x * -6i) + 3iX * (3i + x) + 6ix * (3i + x) + -3ixX * (3i + x) + 2x * (3i + x) + -1xX * (3i + x) + -2x2 * (3i + x) + x2X(3i + x)) = 0

Reorder the terms:
((-6ix + -18i2) + 3iX * (3i + x) + 6ix * (3i + x) + -3ixX * (3i + x) + 2x * (3i + x) + -1xX * (3i + x) + -2x2 * (3i + x) + x2X(3i + x)) = 0
((-6ix + -18i2) + 3iX * (3i + x) + 6ix * (3i + x) + -3ixX * (3i + x) + 2x * (3i + x) + -1xX * (3i + x) + -2x2 * (3i + x) + x2X(3i + x)) = 0
(-6ix + -18i2 + (3i * 3iX + x * 3iX) + 6ix * (3i + x) + -3ixX * (3i + x) + 2x * (3i + x) + -1xX * (3i + x) + -2x2 * (3i + x) + x2X(3i + x)) = 0

Reorder the terms:
(-6ix + -18i2 + (3ixX + 9i2X) + 6ix * (3i + x) + -3ixX * (3i + x) + 2x * (3i + x) + -1xX * (3i + x) + -2x2 * (3i + x) + x2X(3i + x)) = 0
(-6ix + -18i2 + (3ixX + 9i2X) + 6ix * (3i + x) + -3ixX * (3i + x) + 2x * (3i + x) + -1xX * (3i + x) + -2x2 * (3i + x) + x2X(3i + x)) = 0
(-6ix + -18i2 + 3ixX + 9i2X + (3i * 6ix + x * 6ix) + -3ixX * (3i + x) + 2x * (3i + x) + -1xX * (3i + x) + -2x2 * (3i + x) + x2X(3i + x)) = 0

Reorder the terms:
(-6ix + -18i2 + 3ixX + 9i2X + (6ix2 + 18i2x) + -3ixX * (3i + x) + 2x * (3i + x) + -1xX * (3i + x) + -2x2 * (3i + x) + x2X(3i + x)) = 0
(-6ix + -18i2 + 3ixX + 9i2X + (6ix2 + 18i2x) + -3ixX * (3i + x) + 2x * (3i + x) + -1xX * (3i + x) + -2x2 * (3i + x) + x2X(3i + x)) = 0
(-6ix + -18i2 + 3ixX + 9i2X + 6ix2 + 18i2x + (3i * -3ixX + x * -3ixX) + 2x * (3i + x) + -1xX * (3i + x) + -2x2 * (3i + x) + x2X(3i + x)) = 0

Reorder the terms:
(-6ix + -18i2 + 3ixX + 9i2X + 6ix2 + 18i2x + (-3ix2X + -9i2xX) + 2x * (3i + x) + -1xX * (3i + x) + -2x2 * (3i + x) + x2X(3i + x)) = 0
(-6ix + -18i2 + 3ixX + 9i2X + 6ix2 + 18i2x + (-3ix2X + -9i2xX) + 2x * (3i + x) + -1xX * (3i + x) + -2x2 * (3i + x) + x2X(3i + x)) = 0
(-6ix + -18i2 + 3ixX + 9i2X + 6ix2 + 18i2x + -3ix2X + -9i2xX + (3i * 2x + x * 2x) + -1xX * (3i + x) + -2x2 * (3i + x) + x2X(3i + x)) = 0
(-6ix + -18i2 + 3ixX + 9i2X + 6ix2 + 18i2x + -3ix2X + -9i2xX + (6ix + 2x2) + -1xX * (3i + x) + -2x2 * (3i + x) + x2X(3i + x)) = 0
(-6ix + -18i2 + 3ixX + 9i2X + 6ix2 + 18i2x + -3ix2X + -9i2xX + 6ix + 2x2 + (3i * -1xX + x * -1xX) + -2x2 * (3i + x) + x2X(3i + x)) = 0
(-6ix + -18i2 + 3ixX + 9i2X + 6ix2 + 18i2x + -3ix2X + -9i2xX + 6ix + 2x2 + (-3ixX + -1x2X) + -2x2 * (3i + x) + x2X(3i + x)) = 0
(-6ix + -18i2 + 3ixX + 9i2X + 6ix2 + 18i2x + -3ix2X + -9i2xX + 6ix + 2x2 + -3ixX + -1x2X + (3i * -2x2 + x * -2x2) + x2X(3i + x)) = 0
(-6ix + -18i2 + 3ixX + 9i2X + 6ix2 + 18i2x + -3ix2X + -9i2xX + 6ix + 2x2 + -3ixX + -1x2X + (-6ix2 + -2x3) + x2X(3i + x)) = 0
(-6ix + -18i2 + 3ixX + 9i2X + 6ix2 + 18i2x + -3ix2X + -9i2xX + 6ix + 2x2 + -3ixX + -1x2X + -6ix2 + -2x3 + (3i * x2X + x * x2X)) = 0
(-6ix + -18i2 + 3ixX + 9i2X + 6ix2 + 18i2x + -3ix2X + -9i2xX + 6ix + 2x2 + -3ixX + -1x2X + -6ix2 + -2x3 + (3ix2X + x3X)) = 0

Reorder the terms:
(-6ix + 6ix + 3ixX + -3ixX + 6ix2 + -6ix2 + -3ix2X + 3ix2X + -18i2 + 9i2X + 18i2x + -9i2xX + 2x2 + -1x2X + -2x3 + x3X) = 0

Combine like terms: -6ix + 6ix = 0
(0 + 3ixX + -3ixX + 6ix2 + -6ix2 + -3ix2X + 3ix2X + -18i2 + 9i2X + 18i2x + -9i2xX + 2x2 + -1x2X + -2x3 + x3X) = 0
(3ixX + -3ixX + 6ix2 + -6ix2 + -3ix2X + 3ix2X + -18i2 + 9i2X + 18i2x + -9i2xX + 2x2 + -1x2X + -2x3 + x3X) = 0

Combine like terms: 3ixX + -3ixX = 0
(0 + 6ix2 + -6ix2 + -3ix2X + 3ix2X + -18i2 + 9i2X + 18i2x + -9i2xX + 2x2 + -1x2X + -2x3 + x3X) = 0
(6ix2 + -6ix2 + -3ix2X + 3ix2X + -18i2 + 9i2X + 18i2x + -9i2xX + 2x2 + -1x2X + -2x3 + x3X) = 0

Combine like terms: 6ix2 + -6ix2 = 0
(0 + -3ix2X + 3ix2X + -18i2 + 9i2X + 18i2x + -9i2xX + 2x2 + -1x2X + -2x3 + x3X) = 0
(-3ix2X + 3ix2X + -18i2 + 9i2X + 18i2x + -9i2xX + 2x2 + -1x2X + -2x3 + x3X) = 0

Combine like terms: -3ix2X + 3ix2X = 0
(0 + -18i2 + 9i2X + 18i2x + -9i2xX + 2x2 + -1x2X + -2x3 + x3X) = 0
(-18i2 + 9i2X + 18i2x + -9i2xX + 2x2 + -1x2X + -2x3 + x3X) = 0

Solving
-18i2 + 9i2X + 18i2x + -9i2xX + 2x2 + -1x2X + -2x3 + x3X = 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.
-18i2 + 9i2X + 18i2x + -9i2xX + 2x2 + -1x2X + -2x3 + -2x2 + x3X = 0 + -2x2

Reorder the terms:
-18i2 + 9i2X + 18i2x + -9i2xX + 2x2 + -2x2 + -1x2X + -2x3 + x3X = 0 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-18i2 + 9i2X + 18i2x + -9i2xX + 0 + -1x2X + -2x3 + x3X = 0 + -2x2
-18i2 + 9i2X + 18i2x + -9i2xX + -1x2X + -2x3 + x3X = 0 + -2x2
Remove the zero:
-18i2 + 9i2X + 18i2x + -9i2xX + -1x2X + -2x3 + x3X = -2x2

Add 'x2X' to each side of the equation.
-18i2 + 9i2X + 18i2x + -9i2xX + -1x2X + -2x3 + x2X + x3X = -2x2 + x2X

Reorder the terms:
-18i2 + 9i2X + 18i2x + -9i2xX + -1x2X + x2X + -2x3 + x3X = -2x2 + x2X

Combine like terms: -1x2X + x2X = 0
-18i2 + 9i2X + 18i2x + -9i2xX + 0 + -2x3 + x3X = -2x2 + x2X
-18i2 + 9i2X + 18i2x + -9i2xX + -2x3 + x3X = -2x2 + x2X

Add '2x3' to each side of the equation.
-18i2 + 9i2X + 18i2x + -9i2xX + -2x3 + 2x3 + x3X = -2x2 + x2X + 2x3

Combine like terms: -2x3 + 2x3 = 0
-18i2 + 9i2X + 18i2x + -9i2xX + 0 + x3X = -2x2 + x2X + 2x3
-18i2 + 9i2X + 18i2x + -9i2xX + x3X = -2x2 + x2X + 2x3

Add '-1x3X' to each side of the equation.
-18i2 + 9i2X + 18i2x + -9i2xX + x3X + -1x3X = -2x2 + x2X + 2x3 + -1x3X

Combine like terms: x3X + -1x3X = 0
-18i2 + 9i2X + 18i2x + -9i2xX + 0 = -2x2 + x2X + 2x3 + -1x3X
-18i2 + 9i2X + 18i2x + -9i2xX = -2x2 + x2X + 2x3 + -1x3X

Reorder the terms:
-18i2 + 9i2X + 18i2x + -9i2xX + 2x2 + -1x2X + -2x3 + x3X = -2x2 + 2x2 + x2X + -1x2X + 2x3 + -2x3 + -1x3X + x3X

Combine like terms: -2x2 + 2x2 = 0
-18i2 + 9i2X + 18i2x + -9i2xX + 2x2 + -1x2X + -2x3 + x3X = 0 + x2X + -1x2X + 2x3 + -2x3 + -1x3X + x3X
-18i2 + 9i2X + 18i2x + -9i2xX + 2x2 + -1x2X + -2x3 + x3X = x2X + -1x2X + 2x3 + -2x3 + -1x3X + x3X

Combine like terms: x2X + -1x2X = 0
-18i2 + 9i2X + 18i2x + -9i2xX + 2x2 + -1x2X + -2x3 + x3X = 0 + 2x3 + -2x3 + -1x3X + x3X
-18i2 + 9i2X + 18i2x + -9i2xX + 2x2 + -1x2X + -2x3 + x3X = 2x3 + -2x3 + -1x3X + x3X

Combine like terms: 2x3 + -2x3 = 0
-18i2 + 9i2X + 18i2x + -9i2xX + 2x2 + -1x2X + -2x3 + x3X = 0 + -1x3X + x3X
-18i2 + 9i2X + 18i2x + -9i2xX + 2x2 + -1x2X + -2x3 + x3X = -1x3X + x3X

Combine like terms: -1x3X + x3X = 0
-18i2 + 9i2X + 18i2x + -9i2xX + 2x2 + -1x2X + -2x3 + x3X = 0

The solution to this equation could not be determined.

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