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

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


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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

The solution to this equation could not be determined.

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