f(x)=(x-3)(x-5i)(x-6i)

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Solution for f(x)=(x-3)(x-5i)(x-6i) equation: 


Simplifying
f(x) = (x + -3)(x + -5i)(x + -6i)

Multiply f * x
fx = (x + -3)(x + -5i)(x + -6i)

Reorder the terms:
fx = (-3 + x)(x + -5i)(x + -6i)

Reorder the terms:
fx = (-3 + x)(-5i + x)(x + -6i)

Reorder the terms:
fx = (-3 + x)(-5i + x)(-6i + x)

Multiply (-3 + x) * (-5i + x)
fx = (-3(-5i + x) + x(-5i + x))(-6i + x)
fx = ((-5i * -3 + x * -3) + x(-5i + x))(-6i + x)
fx = ((15i + -3x) + x(-5i + x))(-6i + x)
fx = (15i + -3x + (-5i * x + x * x))(-6i + x)
fx = (15i + -3x + (-5ix + x2))(-6i + x)

Reorder the terms:
fx = (15i + -5ix + -3x + x2)(-6i + x)
fx = (15i + -5ix + -3x + x2)(-6i + x)

Multiply (15i + -5ix + -3x + x2) * (-6i + x)
fx = (15i * (-6i + x) + -5ix * (-6i + x) + -3x * (-6i + x) + x2(-6i + x))
fx = ((-6i * 15i + x * 15i) + -5ix * (-6i + x) + -3x * (-6i + x) + x2(-6i + x))

Reorder the terms:
fx = ((15ix + -90i2) + -5ix * (-6i + x) + -3x * (-6i + x) + x2(-6i + x))
fx = ((15ix + -90i2) + -5ix * (-6i + x) + -3x * (-6i + x) + x2(-6i + x))
fx = (15ix + -90i2 + (-6i * -5ix + x * -5ix) + -3x * (-6i + x) + x2(-6i + x))

Reorder the terms:
fx = (15ix + -90i2 + (-5ix2 + 30i2x) + -3x * (-6i + x) + x2(-6i + x))
fx = (15ix + -90i2 + (-5ix2 + 30i2x) + -3x * (-6i + x) + x2(-6i + x))
fx = (15ix + -90i2 + -5ix2 + 30i2x + (-6i * -3x + x * -3x) + x2(-6i + x))
fx = (15ix + -90i2 + -5ix2 + 30i2x + (18ix + -3x2) + x2(-6i + x))
fx = (15ix + -90i2 + -5ix2 + 30i2x + 18ix + -3x2 + (-6i * x2 + x * x2))
fx = (15ix + -90i2 + -5ix2 + 30i2x + 18ix + -3x2 + (-6ix2 + x3))

Reorder the terms:
fx = (15ix + 18ix + -5ix2 + -6ix2 + -90i2 + 30i2x + -3x2 + x3)

Combine like terms: 15ix + 18ix = 33ix
fx = (33ix + -5ix2 + -6ix2 + -90i2 + 30i2x + -3x2 + x3)

Combine like terms: -5ix2 + -6ix2 = -11ix2
fx = (33ix + -11ix2 + -90i2 + 30i2x + -3x2 + x3)

Solving
fx = 33ix + -11ix2 + -90i2 + 30i2x + -3x2 + x3

Solving for variable 'f'.

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

Divide each side by 'x'.
f = 33i + -11ix + -90i2x-1 + 30i2 + -3x + x2

Simplifying
f = 33i + -11ix + -90i2x-1 + 30i2 + -3x + x2

Reorder the terms:
f = 33i + -11ix + 30i2 + -90i2x-1 + -3x + x2

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