(x+2)(x-4)(x+3i)(x-3i)=0

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Solution for (x+2)(x-4)(x+3i)(x-3i)=0 equation: 


Simplifying
(x + 2)(x + -4)(x + 3i)(x + -3i) = 0

Reorder the terms:
(2 + x)(x + -4)(x + 3i)(x + -3i) = 0

Reorder the terms:
(2 + x)(-4 + x)(x + 3i)(x + -3i) = 0

Reorder the terms:
(2 + x)(-4 + x)(3i + x)(x + -3i) = 0

Reorder the terms:
(2 + x)(-4 + x)(3i + x)(-3i + x) = 0

Multiply (2 + x) * (-4 + x)
(2(-4 + x) + x(-4 + x))(3i + x)(-3i + x) = 0
((-4 * 2 + x * 2) + x(-4 + x))(3i + x)(-3i + x) = 0
((-8 + 2x) + x(-4 + x))(3i + x)(-3i + x) = 0
(-8 + 2x + (-4 * x + x * x))(3i + x)(-3i + x) = 0
(-8 + 2x + (-4x + x2))(3i + x)(-3i + x) = 0

Combine like terms: 2x + -4x = -2x
(-8 + -2x + x2)(3i + x)(-3i + x) = 0

Multiply (-8 + -2x + x2) * (3i + x)
(-8(3i + x) + -2x * (3i + x) + x2(3i + x))(-3i + x) = 0
((3i * -8 + x * -8) + -2x * (3i + x) + x2(3i + x))(-3i + x) = 0
((-24i + -8x) + -2x * (3i + x) + x2(3i + x))(-3i + x) = 0
(-24i + -8x + (3i * -2x + x * -2x) + x2(3i + x))(-3i + x) = 0
(-24i + -8x + (-6ix + -2x2) + x2(3i + x))(-3i + x) = 0
(-24i + -8x + -6ix + -2x2 + (3i * x2 + x * x2))(-3i + x) = 0
(-24i + -8x + -6ix + -2x2 + (3ix2 + x3))(-3i + x) = 0

Reorder the terms:
(-24i + -6ix + 3ix2 + -8x + -2x2 + x3)(-3i + x) = 0
(-24i + -6ix + 3ix2 + -8x + -2x2 + x3)(-3i + x) = 0

Multiply (-24i + -6ix + 3ix2 + -8x + -2x2 + x3) * (-3i + x)
(-24i * (-3i + x) + -6ix * (-3i + x) + 3ix2 * (-3i + x) + -8x * (-3i + x) + -2x2 * (-3i + x) + x3(-3i + x)) = 0
((-3i * -24i + x * -24i) + -6ix * (-3i + x) + 3ix2 * (-3i + x) + -8x * (-3i + x) + -2x2 * (-3i + x) + x3(-3i + x)) = 0

Reorder the terms:
((-24ix + 72i2) + -6ix * (-3i + x) + 3ix2 * (-3i + x) + -8x * (-3i + x) + -2x2 * (-3i + x) + x3(-3i + x)) = 0
((-24ix + 72i2) + -6ix * (-3i + x) + 3ix2 * (-3i + x) + -8x * (-3i + x) + -2x2 * (-3i + x) + x3(-3i + x)) = 0
(-24ix + 72i2 + (-3i * -6ix + x * -6ix) + 3ix2 * (-3i + x) + -8x * (-3i + x) + -2x2 * (-3i + x) + x3(-3i + x)) = 0

Reorder the terms:
(-24ix + 72i2 + (-6ix2 + 18i2x) + 3ix2 * (-3i + x) + -8x * (-3i + x) + -2x2 * (-3i + x) + x3(-3i + x)) = 0
(-24ix + 72i2 + (-6ix2 + 18i2x) + 3ix2 * (-3i + x) + -8x * (-3i + x) + -2x2 * (-3i + x) + x3(-3i + x)) = 0
(-24ix + 72i2 + -6ix2 + 18i2x + (-3i * 3ix2 + x * 3ix2) + -8x * (-3i + x) + -2x2 * (-3i + x) + x3(-3i + x)) = 0

Reorder the terms:
(-24ix + 72i2 + -6ix2 + 18i2x + (3ix3 + -9i2x2) + -8x * (-3i + x) + -2x2 * (-3i + x) + x3(-3i + x)) = 0
(-24ix + 72i2 + -6ix2 + 18i2x + (3ix3 + -9i2x2) + -8x * (-3i + x) + -2x2 * (-3i + x) + x3(-3i + x)) = 0
(-24ix + 72i2 + -6ix2 + 18i2x + 3ix3 + -9i2x2 + (-3i * -8x + x * -8x) + -2x2 * (-3i + x) + x3(-3i + x)) = 0
(-24ix + 72i2 + -6ix2 + 18i2x + 3ix3 + -9i2x2 + (24ix + -8x2) + -2x2 * (-3i + x) + x3(-3i + x)) = 0
(-24ix + 72i2 + -6ix2 + 18i2x + 3ix3 + -9i2x2 + 24ix + -8x2 + (-3i * -2x2 + x * -2x2) + x3(-3i + x)) = 0
(-24ix + 72i2 + -6ix2 + 18i2x + 3ix3 + -9i2x2 + 24ix + -8x2 + (6ix2 + -2x3) + x3(-3i + x)) = 0
(-24ix + 72i2 + -6ix2 + 18i2x + 3ix3 + -9i2x2 + 24ix + -8x2 + 6ix2 + -2x3 + (-3i * x3 + x * x3)) = 0
(-24ix + 72i2 + -6ix2 + 18i2x + 3ix3 + -9i2x2 + 24ix + -8x2 + 6ix2 + -2x3 + (-3ix3 + x4)) = 0

Reorder the terms:
(-24ix + 24ix + -6ix2 + 6ix2 + 3ix3 + -3ix3 + 72i2 + 18i2x + -9i2x2 + -8x2 + -2x3 + x4) = 0

Combine like terms: -24ix + 24ix = 0
(0 + -6ix2 + 6ix2 + 3ix3 + -3ix3 + 72i2 + 18i2x + -9i2x2 + -8x2 + -2x3 + x4) = 0
(-6ix2 + 6ix2 + 3ix3 + -3ix3 + 72i2 + 18i2x + -9i2x2 + -8x2 + -2x3 + x4) = 0

Combine like terms: -6ix2 + 6ix2 = 0
(0 + 3ix3 + -3ix3 + 72i2 + 18i2x + -9i2x2 + -8x2 + -2x3 + x4) = 0
(3ix3 + -3ix3 + 72i2 + 18i2x + -9i2x2 + -8x2 + -2x3 + x4) = 0

Combine like terms: 3ix3 + -3ix3 = 0
(0 + 72i2 + 18i2x + -9i2x2 + -8x2 + -2x3 + x4) = 0
(72i2 + 18i2x + -9i2x2 + -8x2 + -2x3 + x4) = 0

Solving
72i2 + 18i2x + -9i2x2 + -8x2 + -2x3 + x4 = 0

Solving for variable 'i'.

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

Add '8x2' to each side of the equation.
72i2 + 18i2x + -9i2x2 + -8x2 + -2x3 + 8x2 + x4 = 0 + 8x2

Reorder the terms:
72i2 + 18i2x + -9i2x2 + -8x2 + 8x2 + -2x3 + x4 = 0 + 8x2

Combine like terms: -8x2 + 8x2 = 0
72i2 + 18i2x + -9i2x2 + 0 + -2x3 + x4 = 0 + 8x2
72i2 + 18i2x + -9i2x2 + -2x3 + x4 = 0 + 8x2
Remove the zero:
72i2 + 18i2x + -9i2x2 + -2x3 + x4 = 8x2

Add '2x3' to each side of the equation.
72i2 + 18i2x + -9i2x2 + -2x3 + 2x3 + x4 = 8x2 + 2x3

Combine like terms: -2x3 + 2x3 = 0
72i2 + 18i2x + -9i2x2 + 0 + x4 = 8x2 + 2x3
72i2 + 18i2x + -9i2x2 + x4 = 8x2 + 2x3

Add '-1x4' to each side of the equation.
72i2 + 18i2x + -9i2x2 + x4 + -1x4 = 8x2 + 2x3 + -1x4

Combine like terms: x4 + -1x4 = 0
72i2 + 18i2x + -9i2x2 + 0 = 8x2 + 2x3 + -1x4
72i2 + 18i2x + -9i2x2 = 8x2 + 2x3 + -1x4

Reorder the terms:
72i2 + 18i2x + -9i2x2 + -8x2 + -2x3 + x4 = 8x2 + -8x2 + 2x3 + -2x3 + -1x4 + x4

Combine like terms: 8x2 + -8x2 = 0
72i2 + 18i2x + -9i2x2 + -8x2 + -2x3 + x4 = 0 + 2x3 + -2x3 + -1x4 + x4
72i2 + 18i2x + -9i2x2 + -8x2 + -2x3 + x4 = 2x3 + -2x3 + -1x4 + x4

Combine like terms: 2x3 + -2x3 = 0
72i2 + 18i2x + -9i2x2 + -8x2 + -2x3 + x4 = 0 + -1x4 + x4
72i2 + 18i2x + -9i2x2 + -8x2 + -2x3 + x4 = -1x4 + x4

Combine like terms: -1x4 + x4 = 0
72i2 + 18i2x + -9i2x2 + -8x2 + -2x3 + x4 = 0

The solution to this equation could not be determined.

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