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

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


Simplifying
(x2 + -3x + 2)(x + -3i)(x + 3i) = 0

Reorder the terms:
(2 + -3x + x2)(x + -3i)(x + 3i) = 0

Reorder the terms:
(2 + -3x + x2)(-3i + x)(x + 3i) = 0

Reorder the terms:
(2 + -3x + x2)(-3i + x)(3i + x) = 0

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

The solution to this equation could not be determined.

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