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

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


Simplifying
f(x) = (x + (2 + i))(x + -1(2 + i))

Multiply f * x
fx = (x + (2 + i))(x + -1(2 + i))

Remove parenthesis around (2 + i)
fx = (x + 2 + i)(x + -1(2 + i))

Reorder the terms:
fx = (2 + i + x)(x + -1(2 + i))
fx = (2 + i + x)(x + (2 * -1 + i * -1))
fx = (2 + i + x)(x + (-2 + -1i))

Reorder the terms:
fx = (2 + i + x)(-2 + -1i + x)

Multiply (2 + i + x) * (-2 + -1i + x)
fx = (2(-2 + -1i + x) + i(-2 + -1i + x) + x(-2 + -1i + x))
fx = ((-2 * 2 + -1i * 2 + x * 2) + i(-2 + -1i + x) + x(-2 + -1i + x))
fx = ((-4 + -2i + 2x) + i(-2 + -1i + x) + x(-2 + -1i + x))
fx = (-4 + -2i + 2x + (-2 * i + -1i * i + x * i) + x(-2 + -1i + x))

Reorder the terms:
fx = (-4 + -2i + 2x + (-2i + ix + -1i2) + x(-2 + -1i + x))
fx = (-4 + -2i + 2x + (-2i + ix + -1i2) + x(-2 + -1i + x))
fx = (-4 + -2i + 2x + -2i + ix + -1i2 + (-2 * x + -1i * x + x * x))

Reorder the terms:
fx = (-4 + -2i + 2x + -2i + ix + -1i2 + (-1ix + -2x + x2))
fx = (-4 + -2i + 2x + -2i + ix + -1i2 + (-1ix + -2x + x2))

Reorder the terms:
fx = (-4 + -2i + -2i + ix + -1ix + -1i2 + 2x + -2x + x2)

Combine like terms: -2i + -2i = -4i
fx = (-4 + -4i + ix + -1ix + -1i2 + 2x + -2x + x2)

Combine like terms: ix + -1ix = 0
fx = (-4 + -4i + 0 + -1i2 + 2x + -2x + x2)
fx = (-4 + -4i + -1i2 + 2x + -2x + x2)

Combine like terms: 2x + -2x = 0
fx = (-4 + -4i + -1i2 + 0 + x2)
fx = (-4 + -4i + -1i2 + x2)

Solving
fx = -4 + -4i + -1i2 + 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 = -4x-1 + -4ix-1 + -1i2x-1 + x

Simplifying
f = -4x-1 + -4ix-1 + -1i2x-1 + x

Reorder the terms:
f = -4ix-1 + -1i2x-1 + -4x-1 + x

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