(x^2+2x+2)=((x+1-i)(x+1+i))

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Solution for (x^2+2x+2)=((x+1-i)(x+1+i)) equation: 


Simplifying
(x2 + 2x + 2) = ((x + 1 + -1i)(x + 1 + i))

Reorder the terms:
(2 + 2x + x2) = ((x + 1 + -1i)(x + 1 + i))

Remove parenthesis around (2 + 2x + x2)
2 + 2x + x2 = ((x + 1 + -1i)(x + 1 + i))

Reorder the terms:
2 + 2x + x2 = ((1 + -1i + x)(x + 1 + i))

Reorder the terms:
2 + 2x + x2 = ((1 + -1i + x)(1 + i + x))

Multiply (1 + -1i + x) * (1 + i + x)
2 + 2x + x2 = ((1(1 + i + x) + -1i * (1 + i + x) + x(1 + i + x)))
2 + 2x + x2 = (((1 * 1 + i * 1 + x * 1) + -1i * (1 + i + x) + x(1 + i + x)))
2 + 2x + x2 = (((1 + 1i + 1x) + -1i * (1 + i + x) + x(1 + i + x)))
2 + 2x + x2 = ((1 + 1i + 1x + (1 * -1i + i * -1i + x * -1i) + x(1 + i + x)))

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

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

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

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

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

Combine like terms: 1x + 1x = 2x
2 + 2x + x2 = ((1 + -1i2 + 2x + x2))
2 + 2x + x2 = (1 + -1i2 + 2x + x2)

Remove parenthesis around (1 + -1i2 + 2x + x2)
2 + 2x + x2 = 1 + -1i2 + 2x + x2

Add '-2x' to each side of the equation.
2 + 2x + -2x + x2 = 1 + -1i2 + 2x + -2x + x2

Combine like terms: 2x + -2x = 0
2 + 0 + x2 = 1 + -1i2 + 2x + -2x + x2
2 + x2 = 1 + -1i2 + 2x + -2x + x2

Combine like terms: 2x + -2x = 0
2 + x2 = 1 + -1i2 + 0 + x2
2 + x2 = 1 + -1i2 + x2

Add '-1x2' to each side of the equation.
2 + x2 + -1x2 = 1 + -1i2 + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
2 + 0 = 1 + -1i2 + x2 + -1x2
2 = 1 + -1i2 + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
2 = 1 + -1i2 + 0
2 = 1 + -1i2

Solving
2 = 1 + -1i2

Solving for variable 'i'.

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

Add 'i2' to each side of the equation.
2 + i2 = 1 + -1i2 + i2

Combine like terms: -1i2 + i2 = 0
2 + i2 = 1 + 0
2 + i2 = 1

Add '-2' to each side of the equation.
2 + -2 + i2 = 1 + -2

Combine like terms: 2 + -2 = 0
0 + i2 = 1 + -2
i2 = 1 + -2

Combine like terms: 1 + -2 = -1
i2 = -1

Simplifying
i2 = -1

Reorder the terms:
1 + i2 = -1 + 1

Combine like terms: -1 + 1 = 0
1 + i2 = 0

The solution to this equation could not be determined.

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