p(x)=[x-(1+i)][x-(1-i)]

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Solution for p(x)=[x-(1+i)][x-(1-i)] equation: 


Simplifying
p(x) = [x + -1(1 + i)][x + -1(1 + -1i)]

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

Reorder the terms:
px = [-1 + -1i + x][x + -1(1 + -1i)]
px = [-1 + -1i + x][x + (1 * -1 + -1i * -1)]
px = [-1 + -1i + x][x + (-1 + 1i)]

Reorder the terms:
px = [-1 + -1i + x][-1 + 1i + x]

Multiply [-1 + -1i + x] * [-1 + 1i + x]
px = [-1[-1 + 1i + x] + -1i * [-1 + 1i + x] + x[-1 + 1i + x]]
px = [[-1 * -1 + 1i * -1 + x * -1] + -1i * [-1 + 1i + x] + x[-1 + 1i + x]]
px = [[1 + -1i + -1x] + -1i * [-1 + 1i + x] + x[-1 + 1i + x]]
px = [1 + -1i + -1x + [-1 * -1i + 1i * -1i + x * -1i] + x[-1 + 1i + x]]

Reorder the terms:
px = [1 + -1i + -1x + [1i + -1ix + -1i2] + x[-1 + 1i + x]]
px = [1 + -1i + -1x + [1i + -1ix + -1i2] + x[-1 + 1i + x]]
px = [1 + -1i + -1x + 1i + -1ix + -1i2 + [-1 * x + 1i * x + x * x]]

Reorder the terms:
px = [1 + -1i + -1x + 1i + -1ix + -1i2 + [1ix + -1x + x2]]
px = [1 + -1i + -1x + 1i + -1ix + -1i2 + [1ix + -1x + x2]]

Reorder the terms:
px = [1 + -1i + 1i + -1ix + 1ix + -1i2 + -1x + -1x + x2]

Combine like terms: -1i + 1i = 0
px = [1 + 0 + -1ix + 1ix + -1i2 + -1x + -1x + x2]
px = [1 + -1ix + 1ix + -1i2 + -1x + -1x + x2]

Combine like terms: -1ix + 1ix = 0
px = [1 + 0 + -1i2 + -1x + -1x + x2]
px = [1 + -1i2 + -1x + -1x + x2]

Combine like terms: -1x + -1x = -2x
px = [1 + -1i2 + -2x + x2]

Solving
px = 1 + -1i2 + -2x + 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 = x-1 + -1i2x-1 + -2 + x

Simplifying
p = x-1 + -1i2x-1 + -2 + x

Reorder the terms:
p = -2 + -1i2x-1 + x-1 + x

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