(x-5)(x-3i)(x+3i)=0

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Solution for (x-5)(x-3i)(x+3i)=0 equation: 


Simplifying
(x + -5)(x + -3i)(x + 3i) = 0

Reorder the terms:
(-5 + x)(x + -3i)(x + 3i) = 0

Reorder the terms:
(-5 + x)(-3i + x)(x + 3i) = 0

Reorder the terms:
(-5 + x)(-3i + x)(3i + x) = 0

Multiply (-5 + x) * (-3i + x)
(-5(-3i + x) + x(-3i + x))(3i + x) = 0
((-3i * -5 + x * -5) + x(-3i + x))(3i + x) = 0
((15i + -5x) + x(-3i + x))(3i + x) = 0
(15i + -5x + (-3i * x + x * x))(3i + x) = 0
(15i + -5x + (-3ix + x2))(3i + x) = 0

Reorder the terms:
(15i + -3ix + -5x + x2)(3i + x) = 0
(15i + -3ix + -5x + x2)(3i + x) = 0

Multiply (15i + -3ix + -5x + x2) * (3i + x)
(15i * (3i + x) + -3ix * (3i + x) + -5x * (3i + x) + x2(3i + x)) = 0
((3i * 15i + x * 15i) + -3ix * (3i + x) + -5x * (3i + x) + x2(3i + x)) = 0

Reorder the terms:
((15ix + 45i2) + -3ix * (3i + x) + -5x * (3i + x) + x2(3i + x)) = 0
((15ix + 45i2) + -3ix * (3i + x) + -5x * (3i + x) + x2(3i + x)) = 0
(15ix + 45i2 + (3i * -3ix + x * -3ix) + -5x * (3i + x) + x2(3i + x)) = 0

Reorder the terms:
(15ix + 45i2 + (-3ix2 + -9i2x) + -5x * (3i + x) + x2(3i + x)) = 0
(15ix + 45i2 + (-3ix2 + -9i2x) + -5x * (3i + x) + x2(3i + x)) = 0
(15ix + 45i2 + -3ix2 + -9i2x + (3i * -5x + x * -5x) + x2(3i + x)) = 0
(15ix + 45i2 + -3ix2 + -9i2x + (-15ix + -5x2) + x2(3i + x)) = 0
(15ix + 45i2 + -3ix2 + -9i2x + -15ix + -5x2 + (3i * x2 + x * x2)) = 0
(15ix + 45i2 + -3ix2 + -9i2x + -15ix + -5x2 + (3ix2 + x3)) = 0

Reorder the terms:
(15ix + -15ix + -3ix2 + 3ix2 + 45i2 + -9i2x + -5x2 + x3) = 0

Combine like terms: 15ix + -15ix = 0
(0 + -3ix2 + 3ix2 + 45i2 + -9i2x + -5x2 + x3) = 0
(-3ix2 + 3ix2 + 45i2 + -9i2x + -5x2 + x3) = 0

Combine like terms: -3ix2 + 3ix2 = 0
(0 + 45i2 + -9i2x + -5x2 + x3) = 0
(45i2 + -9i2x + -5x2 + x3) = 0

Solving
45i2 + -9i2x + -5x2 + x3 = 0

Solving for variable 'i'.

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

Add '5x2' to each side of the equation.
45i2 + -9i2x + -5x2 + 5x2 + x3 = 0 + 5x2

Combine like terms: -5x2 + 5x2 = 0
45i2 + -9i2x + 0 + x3 = 0 + 5x2
45i2 + -9i2x + x3 = 0 + 5x2
Remove the zero:
45i2 + -9i2x + x3 = 5x2

Add '-1x3' to each side of the equation.
45i2 + -9i2x + x3 + -1x3 = 5x2 + -1x3

Combine like terms: x3 + -1x3 = 0
45i2 + -9i2x + 0 = 5x2 + -1x3
45i2 + -9i2x = 5x2 + -1x3

Reorder the terms:
45i2 + -9i2x + -5x2 + x3 = 5x2 + -5x2 + -1x3 + x3

Combine like terms: 5x2 + -5x2 = 0
45i2 + -9i2x + -5x2 + x3 = 0 + -1x3 + x3
45i2 + -9i2x + -5x2 + x3 = -1x3 + x3

Combine like terms: -1x3 + x3 = 0
45i2 + -9i2x + -5x2 + x3 = 0

The solution to this equation could not be determined.

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