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

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


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

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

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

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

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

Multiply (2 + x) * (-1 + x)
(2(-1 + x) + x(-1 + x))(3i + x)(-3i + x) = 0
((-1 * 2 + x * 2) + x(-1 + x))(3i + x)(-3i + x) = 0
((-2 + 2x) + x(-1 + x))(3i + x)(-3i + x) = 0
(-2 + 2x + (-1 * x + x * x))(3i + x)(-3i + x) = 0
(-2 + 2x + (-1x + x2))(3i + x)(-3i + x) = 0

Combine like terms: 2x + -1x = 1x
(-2 + 1x + x2)(3i + x)(-3i + x) = 0

Multiply (-2 + 1x + x2) * (3i + x)
(-2(3i + x) + 1x * (3i + x) + x2(3i + x))(-3i + x) = 0
((3i * -2 + x * -2) + 1x * (3i + x) + x2(3i + x))(-3i + x) = 0
((-6i + -2x) + 1x * (3i + x) + x2(3i + x))(-3i + x) = 0
(-6i + -2x + (3i * 1x + x * 1x) + x2(3i + x))(-3i + x) = 0
(-6i + -2x + (3ix + 1x2) + x2(3i + x))(-3i + x) = 0
(-6i + -2x + 3ix + 1x2 + (3i * x2 + x * x2))(-3i + x) = 0
(-6i + -2x + 3ix + 1x2 + (3ix2 + x3))(-3i + x) = 0

Reorder the terms:
(-6i + 3ix + 3ix2 + -2x + 1x2 + x3)(-3i + x) = 0
(-6i + 3ix + 3ix2 + -2x + 1x2 + x3)(-3i + x) = 0

Multiply (-6i + 3ix + 3ix2 + -2x + 1x2 + x3) * (-3i + x)
(-6i * (-3i + x) + 3ix * (-3i + x) + 3ix2 * (-3i + x) + -2x * (-3i + x) + 1x2 * (-3i + x) + x3(-3i + x)) = 0
((-3i * -6i + x * -6i) + 3ix * (-3i + x) + 3ix2 * (-3i + x) + -2x * (-3i + x) + 1x2 * (-3i + x) + x3(-3i + x)) = 0

Reorder the terms:
((-6ix + 18i2) + 3ix * (-3i + x) + 3ix2 * (-3i + x) + -2x * (-3i + x) + 1x2 * (-3i + x) + x3(-3i + x)) = 0
((-6ix + 18i2) + 3ix * (-3i + x) + 3ix2 * (-3i + x) + -2x * (-3i + x) + 1x2 * (-3i + x) + x3(-3i + x)) = 0
(-6ix + 18i2 + (-3i * 3ix + x * 3ix) + 3ix2 * (-3i + x) + -2x * (-3i + x) + 1x2 * (-3i + x) + x3(-3i + x)) = 0

Reorder the terms:
(-6ix + 18i2 + (3ix2 + -9i2x) + 3ix2 * (-3i + x) + -2x * (-3i + x) + 1x2 * (-3i + x) + x3(-3i + x)) = 0
(-6ix + 18i2 + (3ix2 + -9i2x) + 3ix2 * (-3i + x) + -2x * (-3i + x) + 1x2 * (-3i + x) + x3(-3i + x)) = 0
(-6ix + 18i2 + 3ix2 + -9i2x + (-3i * 3ix2 + x * 3ix2) + -2x * (-3i + x) + 1x2 * (-3i + x) + x3(-3i + x)) = 0

Reorder the terms:
(-6ix + 18i2 + 3ix2 + -9i2x + (3ix3 + -9i2x2) + -2x * (-3i + x) + 1x2 * (-3i + x) + x3(-3i + x)) = 0
(-6ix + 18i2 + 3ix2 + -9i2x + (3ix3 + -9i2x2) + -2x * (-3i + x) + 1x2 * (-3i + x) + x3(-3i + x)) = 0
(-6ix + 18i2 + 3ix2 + -9i2x + 3ix3 + -9i2x2 + (-3i * -2x + x * -2x) + 1x2 * (-3i + x) + x3(-3i + x)) = 0
(-6ix + 18i2 + 3ix2 + -9i2x + 3ix3 + -9i2x2 + (6ix + -2x2) + 1x2 * (-3i + x) + x3(-3i + x)) = 0
(-6ix + 18i2 + 3ix2 + -9i2x + 3ix3 + -9i2x2 + 6ix + -2x2 + (-3i * 1x2 + x * 1x2) + x3(-3i + x)) = 0
(-6ix + 18i2 + 3ix2 + -9i2x + 3ix3 + -9i2x2 + 6ix + -2x2 + (-3ix2 + 1x3) + x3(-3i + x)) = 0
(-6ix + 18i2 + 3ix2 + -9i2x + 3ix3 + -9i2x2 + 6ix + -2x2 + -3ix2 + 1x3 + (-3i * x3 + x * x3)) = 0
(-6ix + 18i2 + 3ix2 + -9i2x + 3ix3 + -9i2x2 + 6ix + -2x2 + -3ix2 + 1x3 + (-3ix3 + x4)) = 0

Reorder the terms:
(-6ix + 6ix + 3ix2 + -3ix2 + 3ix3 + -3ix3 + 18i2 + -9i2x + -9i2x2 + -2x2 + 1x3 + x4) = 0

Combine like terms: -6ix + 6ix = 0
(0 + 3ix2 + -3ix2 + 3ix3 + -3ix3 + 18i2 + -9i2x + -9i2x2 + -2x2 + 1x3 + x4) = 0
(3ix2 + -3ix2 + 3ix3 + -3ix3 + 18i2 + -9i2x + -9i2x2 + -2x2 + 1x3 + x4) = 0

Combine like terms: 3ix2 + -3ix2 = 0
(0 + 3ix3 + -3ix3 + 18i2 + -9i2x + -9i2x2 + -2x2 + 1x3 + x4) = 0
(3ix3 + -3ix3 + 18i2 + -9i2x + -9i2x2 + -2x2 + 1x3 + x4) = 0

Combine like terms: 3ix3 + -3ix3 = 0
(0 + 18i2 + -9i2x + -9i2x2 + -2x2 + 1x3 + x4) = 0
(18i2 + -9i2x + -9i2x2 + -2x2 + 1x3 + x4) = 0

Solving
18i2 + -9i2x + -9i2x2 + -2x2 + 1x3 + x4 = 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 + -9i2x2 + -2x2 + 1x3 + 2x2 + x4 = 0 + 2x2

Reorder the terms:
18i2 + -9i2x + -9i2x2 + -2x2 + 2x2 + 1x3 + x4 = 0 + 2x2

Combine like terms: -2x2 + 2x2 = 0
18i2 + -9i2x + -9i2x2 + 0 + 1x3 + x4 = 0 + 2x2
18i2 + -9i2x + -9i2x2 + 1x3 + x4 = 0 + 2x2
Remove the zero:
18i2 + -9i2x + -9i2x2 + 1x3 + x4 = 2x2

Add '-1x3' to each side of the equation.
18i2 + -9i2x + -9i2x2 + 1x3 + -1x3 + x4 = 2x2 + -1x3

Combine like terms: 1x3 + -1x3 = 0
18i2 + -9i2x + -9i2x2 + 0 + x4 = 2x2 + -1x3
18i2 + -9i2x + -9i2x2 + x4 = 2x2 + -1x3

Add '-1x4' to each side of the equation.
18i2 + -9i2x + -9i2x2 + x4 + -1x4 = 2x2 + -1x3 + -1x4

Combine like terms: x4 + -1x4 = 0
18i2 + -9i2x + -9i2x2 + 0 = 2x2 + -1x3 + -1x4
18i2 + -9i2x + -9i2x2 = 2x2 + -1x3 + -1x4

Reorder the terms:
18i2 + -9i2x + -9i2x2 + -2x2 + x3 + x4 = 2x2 + -2x2 + -1x3 + x3 + -1x4 + x4

Combine like terms: 2x2 + -2x2 = 0
18i2 + -9i2x + -9i2x2 + -2x2 + x3 + x4 = 0 + -1x3 + x3 + -1x4 + x4
18i2 + -9i2x + -9i2x2 + -2x2 + x3 + x4 = -1x3 + x3 + -1x4 + x4

Combine like terms: -1x3 + x3 = 0
18i2 + -9i2x + -9i2x2 + -2x2 + x3 + x4 = 0 + -1x4 + x4
18i2 + -9i2x + -9i2x2 + -2x2 + x3 + x4 = -1x4 + x4

Combine like terms: -1x4 + x4 = 0
18i2 + -9i2x + -9i2x2 + -2x2 + x3 + x4 = 0

The solution to this equation could not be determined.

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