f(x)=4(x-1)(x-3i)(x+3i)

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Solution for f(x)=4(x-1)(x-3i)(x+3i) equation: 


Simplifying
f(x) = 4(x + -1)(x + -3i)(x + 3i)

Multiply f * x
fx = 4(x + -1)(x + -3i)(x + 3i)

Reorder the terms:
fx = 4(-1 + x)(x + -3i)(x + 3i)

Reorder the terms:
fx = 4(-1 + x)(-3i + x)(x + 3i)

Reorder the terms:
fx = 4(-1 + x)(-3i + x)(3i + x)

Multiply (-1 + x) * (-3i + x)
fx = 4(-1(-3i + x) + x(-3i + x))(3i + x)
fx = 4((-3i * -1 + x * -1) + x(-3i + x))(3i + x)
fx = 4((3i + -1x) + x(-3i + x))(3i + x)
fx = 4(3i + -1x + (-3i * x + x * x))(3i + x)
fx = 4(3i + -1x + (-3ix + x2))(3i + x)

Reorder the terms:
fx = 4(3i + -3ix + -1x + x2)(3i + x)
fx = 4(3i + -3ix + -1x + x2)(3i + x)

Multiply (3i + -3ix + -1x + x2) * (3i + x)
fx = 4(3i * (3i + x) + -3ix * (3i + x) + -1x * (3i + x) + x2(3i + x))
fx = 4((3i * 3i + x * 3i) + -3ix * (3i + x) + -1x * (3i + x) + x2(3i + x))

Reorder the terms:
fx = 4((3ix + 9i2) + -3ix * (3i + x) + -1x * (3i + x) + x2(3i + x))
fx = 4((3ix + 9i2) + -3ix * (3i + x) + -1x * (3i + x) + x2(3i + x))
fx = 4(3ix + 9i2 + (3i * -3ix + x * -3ix) + -1x * (3i + x) + x2(3i + x))

Reorder the terms:
fx = 4(3ix + 9i2 + (-3ix2 + -9i2x) + -1x * (3i + x) + x2(3i + x))
fx = 4(3ix + 9i2 + (-3ix2 + -9i2x) + -1x * (3i + x) + x2(3i + x))
fx = 4(3ix + 9i2 + -3ix2 + -9i2x + (3i * -1x + x * -1x) + x2(3i + x))
fx = 4(3ix + 9i2 + -3ix2 + -9i2x + (-3ix + -1x2) + x2(3i + x))
fx = 4(3ix + 9i2 + -3ix2 + -9i2x + -3ix + -1x2 + (3i * x2 + x * x2))
fx = 4(3ix + 9i2 + -3ix2 + -9i2x + -3ix + -1x2 + (3ix2 + x3))

Reorder the terms:
fx = 4(3ix + -3ix + -3ix2 + 3ix2 + 9i2 + -9i2x + -1x2 + x3)

Combine like terms: 3ix + -3ix = 0
fx = 4(0 + -3ix2 + 3ix2 + 9i2 + -9i2x + -1x2 + x3)
fx = 4(-3ix2 + 3ix2 + 9i2 + -9i2x + -1x2 + x3)

Combine like terms: -3ix2 + 3ix2 = 0
fx = 4(0 + 9i2 + -9i2x + -1x2 + x3)
fx = 4(9i2 + -9i2x + -1x2 + x3)
fx = (9i2 * 4 + -9i2x * 4 + -1x2 * 4 + x3 * 4)
fx = (36i2 + -36i2x + -4x2 + 4x3)

Solving
fx = 36i2 + -36i2x + -4x2 + 4x3

Solving for variable 'f'.

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

Divide each side by 'x'.
f = 36i2x-1 + -36i2 + -4x + 4x2

Simplifying
f = 36i2x-1 + -36i2 + -4x + 4x2

Reorder the terms:
f = -36i2 + 36i2x-1 + -4x + 4x2

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