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

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


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

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

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

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

Multiply (4 + 3i + x) * (4 + -3i + x)
fx = (4(4 + -3i + x) + 3i * (4 + -3i + x) + x(4 + -3i + x))
fx = ((4 * 4 + -3i * 4 + x * 4) + 3i * (4 + -3i + x) + x(4 + -3i + x))
fx = ((16 + -12i + 4x) + 3i * (4 + -3i + x) + x(4 + -3i + x))
fx = (16 + -12i + 4x + (4 * 3i + -3i * 3i + x * 3i) + x(4 + -3i + x))

Reorder the terms:
fx = (16 + -12i + 4x + (12i + 3ix + -9i2) + x(4 + -3i + x))
fx = (16 + -12i + 4x + (12i + 3ix + -9i2) + x(4 + -3i + x))
fx = (16 + -12i + 4x + 12i + 3ix + -9i2 + (4 * x + -3i * x + x * x))

Reorder the terms:
fx = (16 + -12i + 4x + 12i + 3ix + -9i2 + (-3ix + 4x + x2))
fx = (16 + -12i + 4x + 12i + 3ix + -9i2 + (-3ix + 4x + x2))

Reorder the terms:
fx = (16 + -12i + 12i + 3ix + -3ix + -9i2 + 4x + 4x + x2)

Combine like terms: -12i + 12i = 0
fx = (16 + 0 + 3ix + -3ix + -9i2 + 4x + 4x + x2)
fx = (16 + 3ix + -3ix + -9i2 + 4x + 4x + x2)

Combine like terms: 3ix + -3ix = 0
fx = (16 + 0 + -9i2 + 4x + 4x + x2)
fx = (16 + -9i2 + 4x + 4x + x2)

Combine like terms: 4x + 4x = 8x
fx = (16 + -9i2 + 8x + x2)

Solving
fx = 16 + -9i2 + 8x + x2

Solving for variable 'f'.

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

Divide each side by 'x'.
f = 16x-1 + -9i2x-1 + 8 + x

Simplifying
f = 16x-1 + -9i2x-1 + 8 + x

Reorder the terms:
f = 8 + -9i2x-1 + 16x-1 + x

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