f(x)=(x+4-5i)(x+4+5i)

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Solution for f(x)=(x+4-5i)(x+4+5i) equation: 


Simplifying
f(x) = (x + 4 + -5i)(x + 4 + 5i)

Multiply f * x
fx = (x + 4 + -5i)(x + 4 + 5i)

Reorder the terms:
fx = (4 + -5i + x)(x + 4 + 5i)

Reorder the terms:
fx = (4 + -5i + x)(4 + 5i + x)

Multiply (4 + -5i + x) * (4 + 5i + x)
fx = (4(4 + 5i + x) + -5i * (4 + 5i + x) + x(4 + 5i + x))
fx = ((4 * 4 + 5i * 4 + x * 4) + -5i * (4 + 5i + x) + x(4 + 5i + x))
fx = ((16 + 20i + 4x) + -5i * (4 + 5i + x) + x(4 + 5i + x))
fx = (16 + 20i + 4x + (4 * -5i + 5i * -5i + x * -5i) + x(4 + 5i + x))

Reorder the terms:
fx = (16 + 20i + 4x + (-20i + -5ix + -25i2) + x(4 + 5i + x))
fx = (16 + 20i + 4x + (-20i + -5ix + -25i2) + x(4 + 5i + x))
fx = (16 + 20i + 4x + -20i + -5ix + -25i2 + (4 * x + 5i * x + x * x))

Reorder the terms:
fx = (16 + 20i + 4x + -20i + -5ix + -25i2 + (5ix + 4x + x2))
fx = (16 + 20i + 4x + -20i + -5ix + -25i2 + (5ix + 4x + x2))

Reorder the terms:
fx = (16 + 20i + -20i + -5ix + 5ix + -25i2 + 4x + 4x + x2)

Combine like terms: 20i + -20i = 0
fx = (16 + 0 + -5ix + 5ix + -25i2 + 4x + 4x + x2)
fx = (16 + -5ix + 5ix + -25i2 + 4x + 4x + x2)

Combine like terms: -5ix + 5ix = 0
fx = (16 + 0 + -25i2 + 4x + 4x + x2)
fx = (16 + -25i2 + 4x + 4x + x2)

Combine like terms: 4x + 4x = 8x
fx = (16 + -25i2 + 8x + x2)

Solving
fx = 16 + -25i2 + 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 + -25i2x-1 + 8 + x

Simplifying
f = 16x-1 + -25i2x-1 + 8 + x

Reorder the terms:
f = 8 + -25i2x-1 + 16x-1 + x

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