(x-(5-2i))(x+(7+4i))=2

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Solution for (x-(5-2i))(x+(7+4i))=2 equation: 


Simplifying
(x + -1(5 + -2i))(x + (7 + 4i)) = 2
(x + (5 * -1 + -2i * -1))(x + (7 + 4i)) = 2
(x + (-5 + 2i))(x + (7 + 4i)) = 2

Reorder the terms:
(-5 + 2i + x)(x + (7 + 4i)) = 2

Remove parenthesis around (7 + 4i)
(-5 + 2i + x)(x + 7 + 4i) = 2

Reorder the terms:
(-5 + 2i + x)(7 + 4i + x) = 2

Multiply (-5 + 2i + x) * (7 + 4i + x)
(-5(7 + 4i + x) + 2i * (7 + 4i + x) + x(7 + 4i + x)) = 2
((7 * -5 + 4i * -5 + x * -5) + 2i * (7 + 4i + x) + x(7 + 4i + x)) = 2
((-35 + -20i + -5x) + 2i * (7 + 4i + x) + x(7 + 4i + x)) = 2
(-35 + -20i + -5x + (7 * 2i + 4i * 2i + x * 2i) + x(7 + 4i + x)) = 2

Reorder the terms:
(-35 + -20i + -5x + (14i + 2ix + 8i2) + x(7 + 4i + x)) = 2
(-35 + -20i + -5x + (14i + 2ix + 8i2) + x(7 + 4i + x)) = 2
(-35 + -20i + -5x + 14i + 2ix + 8i2 + (7 * x + 4i * x + x * x)) = 2

Reorder the terms:
(-35 + -20i + -5x + 14i + 2ix + 8i2 + (4ix + 7x + x2)) = 2
(-35 + -20i + -5x + 14i + 2ix + 8i2 + (4ix + 7x + x2)) = 2

Reorder the terms:
(-35 + -20i + 14i + 2ix + 4ix + 8i2 + -5x + 7x + x2) = 2

Combine like terms: -20i + 14i = -6i
(-35 + -6i + 2ix + 4ix + 8i2 + -5x + 7x + x2) = 2

Combine like terms: 2ix + 4ix = 6ix
(-35 + -6i + 6ix + 8i2 + -5x + 7x + x2) = 2

Combine like terms: -5x + 7x = 2x
(-35 + -6i + 6ix + 8i2 + 2x + x2) = 2

Solving
-35 + -6i + 6ix + 8i2 + 2x + x2 = 2

Solving for variable 'i'.

Reorder the terms:
-35 + -2 + -6i + 6ix + 8i2 + 2x + x2 = 2 + -2

Combine like terms: -35 + -2 = -37
-37 + -6i + 6ix + 8i2 + 2x + x2 = 2 + -2

Combine like terms: 2 + -2 = 0
-37 + -6i + 6ix + 8i2 + 2x + x2 = 0

The solution to this equation could not be determined.

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