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

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


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

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

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

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

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

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

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

Multiply (-3 + -2x + x2) * (3i + x)
(-3(3i + x) + -2x * (3i + x) + x2(3i + x))(-3i + x) = 0
((3i * -3 + x * -3) + -2x * (3i + x) + x2(3i + x))(-3i + x) = 0
((-9i + -3x) + -2x * (3i + x) + x2(3i + x))(-3i + x) = 0
(-9i + -3x + (3i * -2x + x * -2x) + x2(3i + x))(-3i + x) = 0
(-9i + -3x + (-6ix + -2x2) + x2(3i + x))(-3i + x) = 0
(-9i + -3x + -6ix + -2x2 + (3i * x2 + x * x2))(-3i + x) = 0
(-9i + -3x + -6ix + -2x2 + (3ix2 + x3))(-3i + x) = 0

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

Multiply (-9i + -6ix + 3ix2 + -3x + -2x2 + x3) * (-3i + x)
(-9i * (-3i + x) + -6ix * (-3i + x) + 3ix2 * (-3i + x) + -3x * (-3i + x) + -2x2 * (-3i + x) + x3(-3i + x)) = 0
((-3i * -9i + x * -9i) + -6ix * (-3i + x) + 3ix2 * (-3i + x) + -3x * (-3i + x) + -2x2 * (-3i + x) + x3(-3i + x)) = 0

Reorder the terms:
((-9ix + 27i2) + -6ix * (-3i + x) + 3ix2 * (-3i + x) + -3x * (-3i + x) + -2x2 * (-3i + x) + x3(-3i + x)) = 0
((-9ix + 27i2) + -6ix * (-3i + x) + 3ix2 * (-3i + x) + -3x * (-3i + x) + -2x2 * (-3i + x) + x3(-3i + x)) = 0
(-9ix + 27i2 + (-3i * -6ix + x * -6ix) + 3ix2 * (-3i + x) + -3x * (-3i + x) + -2x2 * (-3i + x) + x3(-3i + x)) = 0

Reorder the terms:
(-9ix + 27i2 + (-6ix2 + 18i2x) + 3ix2 * (-3i + x) + -3x * (-3i + x) + -2x2 * (-3i + x) + x3(-3i + x)) = 0
(-9ix + 27i2 + (-6ix2 + 18i2x) + 3ix2 * (-3i + x) + -3x * (-3i + x) + -2x2 * (-3i + x) + x3(-3i + x)) = 0
(-9ix + 27i2 + -6ix2 + 18i2x + (-3i * 3ix2 + x * 3ix2) + -3x * (-3i + x) + -2x2 * (-3i + x) + x3(-3i + x)) = 0

Reorder the terms:
(-9ix + 27i2 + -6ix2 + 18i2x + (3ix3 + -9i2x2) + -3x * (-3i + x) + -2x2 * (-3i + x) + x3(-3i + x)) = 0
(-9ix + 27i2 + -6ix2 + 18i2x + (3ix3 + -9i2x2) + -3x * (-3i + x) + -2x2 * (-3i + x) + x3(-3i + x)) = 0
(-9ix + 27i2 + -6ix2 + 18i2x + 3ix3 + -9i2x2 + (-3i * -3x + x * -3x) + -2x2 * (-3i + x) + x3(-3i + x)) = 0
(-9ix + 27i2 + -6ix2 + 18i2x + 3ix3 + -9i2x2 + (9ix + -3x2) + -2x2 * (-3i + x) + x3(-3i + x)) = 0
(-9ix + 27i2 + -6ix2 + 18i2x + 3ix3 + -9i2x2 + 9ix + -3x2 + (-3i * -2x2 + x * -2x2) + x3(-3i + x)) = 0
(-9ix + 27i2 + -6ix2 + 18i2x + 3ix3 + -9i2x2 + 9ix + -3x2 + (6ix2 + -2x3) + x3(-3i + x)) = 0
(-9ix + 27i2 + -6ix2 + 18i2x + 3ix3 + -9i2x2 + 9ix + -3x2 + 6ix2 + -2x3 + (-3i * x3 + x * x3)) = 0
(-9ix + 27i2 + -6ix2 + 18i2x + 3ix3 + -9i2x2 + 9ix + -3x2 + 6ix2 + -2x3 + (-3ix3 + x4)) = 0

Reorder the terms:
(-9ix + 9ix + -6ix2 + 6ix2 + 3ix3 + -3ix3 + 27i2 + 18i2x + -9i2x2 + -3x2 + -2x3 + x4) = 0

Combine like terms: -9ix + 9ix = 0
(0 + -6ix2 + 6ix2 + 3ix3 + -3ix3 + 27i2 + 18i2x + -9i2x2 + -3x2 + -2x3 + x4) = 0
(-6ix2 + 6ix2 + 3ix3 + -3ix3 + 27i2 + 18i2x + -9i2x2 + -3x2 + -2x3 + x4) = 0

Combine like terms: -6ix2 + 6ix2 = 0
(0 + 3ix3 + -3ix3 + 27i2 + 18i2x + -9i2x2 + -3x2 + -2x3 + x4) = 0
(3ix3 + -3ix3 + 27i2 + 18i2x + -9i2x2 + -3x2 + -2x3 + x4) = 0

Combine like terms: 3ix3 + -3ix3 = 0
(0 + 27i2 + 18i2x + -9i2x2 + -3x2 + -2x3 + x4) = 0
(27i2 + 18i2x + -9i2x2 + -3x2 + -2x3 + x4) = 0

Solving
27i2 + 18i2x + -9i2x2 + -3x2 + -2x3 + x4 = 0

Solving for variable 'i'.

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

Add '3x2' to each side of the equation.
27i2 + 18i2x + -9i2x2 + -3x2 + -2x3 + 3x2 + x4 = 0 + 3x2

Reorder the terms:
27i2 + 18i2x + -9i2x2 + -3x2 + 3x2 + -2x3 + x4 = 0 + 3x2

Combine like terms: -3x2 + 3x2 = 0
27i2 + 18i2x + -9i2x2 + 0 + -2x3 + x4 = 0 + 3x2
27i2 + 18i2x + -9i2x2 + -2x3 + x4 = 0 + 3x2
Remove the zero:
27i2 + 18i2x + -9i2x2 + -2x3 + x4 = 3x2

Add '2x3' to each side of the equation.
27i2 + 18i2x + -9i2x2 + -2x3 + 2x3 + x4 = 3x2 + 2x3

Combine like terms: -2x3 + 2x3 = 0
27i2 + 18i2x + -9i2x2 + 0 + x4 = 3x2 + 2x3
27i2 + 18i2x + -9i2x2 + x4 = 3x2 + 2x3

Add '-1x4' to each side of the equation.
27i2 + 18i2x + -9i2x2 + x4 + -1x4 = 3x2 + 2x3 + -1x4

Combine like terms: x4 + -1x4 = 0
27i2 + 18i2x + -9i2x2 + 0 = 3x2 + 2x3 + -1x4
27i2 + 18i2x + -9i2x2 = 3x2 + 2x3 + -1x4

Reorder the terms:
27i2 + 18i2x + -9i2x2 + -3x2 + -2x3 + x4 = 3x2 + -3x2 + 2x3 + -2x3 + -1x4 + x4

Combine like terms: 3x2 + -3x2 = 0
27i2 + 18i2x + -9i2x2 + -3x2 + -2x3 + x4 = 0 + 2x3 + -2x3 + -1x4 + x4
27i2 + 18i2x + -9i2x2 + -3x2 + -2x3 + x4 = 2x3 + -2x3 + -1x4 + x4

Combine like terms: 2x3 + -2x3 = 0
27i2 + 18i2x + -9i2x2 + -3x2 + -2x3 + x4 = 0 + -1x4 + x4
27i2 + 18i2x + -9i2x2 + -3x2 + -2x3 + x4 = -1x4 + x4

Combine like terms: -1x4 + x4 = 0
27i2 + 18i2x + -9i2x2 + -3x2 + -2x3 + x4 = 0

The solution to this equation could not be determined.

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