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

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


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

Multiply p * x
px = (x + -2 + i)(x + 2 + -1i)

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

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

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

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

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

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

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

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

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

Solving
px = -4 + 4i + -1i2 + x2

Solving for variable 'p'.

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

Divide each side by 'x'.
p = -4x-1 + 4ix-1 + -1i2x-1 + x

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

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

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