f(x)=x^2+(x+2i)(x-2i)

Solution for f(x)=x^2+(x+2i)(x-2i) equation:

Simplifying
f(x) = x2 + (x + 2i)(x + -2i)

Multiply f * x
fx = x2 + (x + 2i)(x + -2i)

Reorder the terms:
fx = x2 + (2i + x)(x + -2i)

Reorder the terms:
fx = x2 + (2i + x)(-2i + x)

Multiply (2i + x) * (-2i + x)
fx = x2 + (2i * (-2i + x) + x(-2i + x))
fx = x2 + ((-2i * 2i + x * 2i) + x(-2i + x))

Reorder the terms:
fx = x2 + ((2ix + -4i2) + x(-2i + x))
fx = x2 + ((2ix + -4i2) + x(-2i + x))
fx = x2 + (2ix + -4i2 + (-2i * x + x * x))
fx = x2 + (2ix + -4i2 + (-2ix + x2))

Reorder the terms:
fx = x2 + (2ix + -2ix + -4i2 + x2)

Combine like terms: 2ix + -2ix = 0
fx = x2 + (0 + -4i2 + x2)
fx = x2 + (-4i2 + x2)

Reorder the terms:
fx = -4i2 + x2 + x2

Combine like terms: x2 + x2 = 2x2
fx = -4i2 + 2x2

Solving
fx = -4i2 + 2x2

Solving for variable 'f'.

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

Divide each side by 'x'.
f = -4i2x-1 + 2x

Simplifying
f = -4i2x-1 + 2x