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

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


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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

The solution to this equation could not be determined.

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