p(x)=[x-(1+2i)][x-(1-2i)](x-2)(x+1)

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Solution for p(x)=[x-(1+2i)][x-(1-2i)](x-2)(x+1) equation: 


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

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

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

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

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

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

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

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

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

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

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

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

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

Multiply [1 + -4i2 + -2x + x2] * (-2 + x)
px = [1(-2 + x) + -4i2 * (-2 + x) + -2x * (-2 + x) + x2(-2 + x)](1 + x)
px = [(-2 * 1 + x * 1) + -4i2 * (-2 + x) + -2x * (-2 + x) + x2(-2 + x)](1 + x)
px = [(-2 + 1x) + -4i2 * (-2 + x) + -2x * (-2 + x) + x2(-2 + x)](1 + x)
px = [-2 + 1x + (-2 * -4i2 + x * -4i2) + -2x * (-2 + x) + x2(-2 + x)](1 + x)
px = [-2 + 1x + (8i2 + -4i2x) + -2x * (-2 + x) + x2(-2 + x)](1 + x)
px = [-2 + 1x + 8i2 + -4i2x + (-2 * -2x + x * -2x) + x2(-2 + x)](1 + x)
px = [-2 + 1x + 8i2 + -4i2x + (4x + -2x2) + x2(-2 + x)](1 + x)
px = [-2 + 1x + 8i2 + -4i2x + 4x + -2x2 + (-2 * x2 + x * x2)](1 + x)
px = [-2 + 1x + 8i2 + -4i2x + 4x + -2x2 + (-2x2 + x3)](1 + x)

Reorder the terms:
px = [-2 + 8i2 + -4i2x + 1x + 4x + -2x2 + -2x2 + x3](1 + x)

Combine like terms: 1x + 4x = 5x
px = [-2 + 8i2 + -4i2x + 5x + -2x2 + -2x2 + x3](1 + x)

Combine like terms: -2x2 + -2x2 = -4x2
px = [-2 + 8i2 + -4i2x + 5x + -4x2 + x3](1 + x)

Multiply [-2 + 8i2 + -4i2x + 5x + -4x2 + x3] * (1 + x)
px = [-2(1 + x) + 8i2 * (1 + x) + -4i2x * (1 + x) + 5x * (1 + x) + -4x2 * (1 + x) + x3(1 + x)]
px = [(1 * -2 + x * -2) + 8i2 * (1 + x) + -4i2x * (1 + x) + 5x * (1 + x) + -4x2 * (1 + x) + x3(1 + x)]
px = [(-2 + -2x) + 8i2 * (1 + x) + -4i2x * (1 + x) + 5x * (1 + x) + -4x2 * (1 + x) + x3(1 + x)]
px = [-2 + -2x + (1 * 8i2 + x * 8i2) + -4i2x * (1 + x) + 5x * (1 + x) + -4x2 * (1 + x) + x3(1 + x)]
px = [-2 + -2x + (8i2 + 8i2x) + -4i2x * (1 + x) + 5x * (1 + x) + -4x2 * (1 + x) + x3(1 + x)]
px = [-2 + -2x + 8i2 + 8i2x + (1 * -4i2x + x * -4i2x) + 5x * (1 + x) + -4x2 * (1 + x) + x3(1 + x)]
px = [-2 + -2x + 8i2 + 8i2x + (-4i2x + -4i2x2) + 5x * (1 + x) + -4x2 * (1 + x) + x3(1 + x)]
px = [-2 + -2x + 8i2 + 8i2x + -4i2x + -4i2x2 + (1 * 5x + x * 5x) + -4x2 * (1 + x) + x3(1 + x)]
px = [-2 + -2x + 8i2 + 8i2x + -4i2x + -4i2x2 + (5x + 5x2) + -4x2 * (1 + x) + x3(1 + x)]
px = [-2 + -2x + 8i2 + 8i2x + -4i2x + -4i2x2 + 5x + 5x2 + (1 * -4x2 + x * -4x2) + x3(1 + x)]
px = [-2 + -2x + 8i2 + 8i2x + -4i2x + -4i2x2 + 5x + 5x2 + (-4x2 + -4x3) + x3(1 + x)]
px = [-2 + -2x + 8i2 + 8i2x + -4i2x + -4i2x2 + 5x + 5x2 + -4x2 + -4x3 + (1 * x3 + x * x3)]
px = [-2 + -2x + 8i2 + 8i2x + -4i2x + -4i2x2 + 5x + 5x2 + -4x2 + -4x3 + (1x3 + x4)]

Reorder the terms:
px = [-2 + 8i2 + 8i2x + -4i2x + -4i2x2 + -2x + 5x + 5x2 + -4x2 + -4x3 + 1x3 + x4]

Combine like terms: 8i2x + -4i2x = 4i2x
px = [-2 + 8i2 + 4i2x + -4i2x2 + -2x + 5x + 5x2 + -4x2 + -4x3 + 1x3 + x4]

Combine like terms: -2x + 5x = 3x
px = [-2 + 8i2 + 4i2x + -4i2x2 + 3x + 5x2 + -4x2 + -4x3 + 1x3 + x4]

Combine like terms: 5x2 + -4x2 = 1x2
px = [-2 + 8i2 + 4i2x + -4i2x2 + 3x + 1x2 + -4x3 + 1x3 + x4]

Combine like terms: -4x3 + 1x3 = -3x3
px = [-2 + 8i2 + 4i2x + -4i2x2 + 3x + 1x2 + -3x3 + x4]

Solving
px = -2 + 8i2 + 4i2x + -4i2x2 + 3x + 1x2 + -3x3 + x4

Solving for variable 'p'.

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

Divide each side by 'x'.
p = -2x-1 + 8i2x-1 + 4i2 + -4i2x + 3 + x + -3x2 + x3

Simplifying
p = -2x-1 + 8i2x-1 + 4i2 + -4i2x + 3 + x + -3x2 + x3

Reorder the terms:
p = 3 + 4i2 + 8i2x-1 + -4i2x + -2x-1 + x + -3x2 + x3

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