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

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


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

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

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

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

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

Multiply (4 + x) * (3i + x)
fx = (4(3i + x) + x(3i + x))(-3i + x)
fx = ((3i * 4 + x * 4) + x(3i + x))(-3i + x)
fx = ((12i + 4x) + x(3i + x))(-3i + x)
fx = (12i + 4x + (3i * x + x * x))(-3i + x)
fx = (12i + 4x + (3ix + x2))(-3i + x)

Reorder the terms:
fx = (12i + 3ix + 4x + x2)(-3i + x)
fx = (12i + 3ix + 4x + x2)(-3i + x)

Multiply (12i + 3ix + 4x + x2) * (-3i + x)
fx = (12i * (-3i + x) + 3ix * (-3i + x) + 4x * (-3i + x) + x2(-3i + x))
fx = ((-3i * 12i + x * 12i) + 3ix * (-3i + x) + 4x * (-3i + x) + x2(-3i + x))

Reorder the terms:
fx = ((12ix + -36i2) + 3ix * (-3i + x) + 4x * (-3i + x) + x2(-3i + x))
fx = ((12ix + -36i2) + 3ix * (-3i + x) + 4x * (-3i + x) + x2(-3i + x))
fx = (12ix + -36i2 + (-3i * 3ix + x * 3ix) + 4x * (-3i + x) + x2(-3i + x))

Reorder the terms:
fx = (12ix + -36i2 + (3ix2 + -9i2x) + 4x * (-3i + x) + x2(-3i + x))
fx = (12ix + -36i2 + (3ix2 + -9i2x) + 4x * (-3i + x) + x2(-3i + x))
fx = (12ix + -36i2 + 3ix2 + -9i2x + (-3i * 4x + x * 4x) + x2(-3i + x))
fx = (12ix + -36i2 + 3ix2 + -9i2x + (-12ix + 4x2) + x2(-3i + x))
fx = (12ix + -36i2 + 3ix2 + -9i2x + -12ix + 4x2 + (-3i * x2 + x * x2))
fx = (12ix + -36i2 + 3ix2 + -9i2x + -12ix + 4x2 + (-3ix2 + x3))

Reorder the terms:
fx = (12ix + -12ix + 3ix2 + -3ix2 + -36i2 + -9i2x + 4x2 + x3)

Combine like terms: 12ix + -12ix = 0
fx = (0 + 3ix2 + -3ix2 + -36i2 + -9i2x + 4x2 + x3)
fx = (3ix2 + -3ix2 + -36i2 + -9i2x + 4x2 + x3)

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

Solving
fx = -36i2 + -9i2x + 4x2 + 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 = -36i2x-1 + -9i2 + 4x + x2

Simplifying
f = -36i2x-1 + -9i2 + 4x + x2

Reorder the terms:
f = -9i2 + -36i2x-1 + 4x + x2

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