(x+(3+2i))(x+(3-2i))=y

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Solution for (x+(3+2i))(x+(3-2i))=y equation: 


Simplifying
(x + (3 + 2i))(x + (3 + -2i)) = y

Remove parenthesis around (3 + 2i)
(x + 3 + 2i)(x + (3 + -2i)) = y

Reorder the terms:
(3 + 2i + x)(x + (3 + -2i)) = y

Remove parenthesis around (3 + -2i)
(3 + 2i + x)(x + 3 + -2i) = y

Reorder the terms:
(3 + 2i + x)(3 + -2i + x) = y

Multiply (3 + 2i + x) * (3 + -2i + x)
(3(3 + -2i + x) + 2i * (3 + -2i + x) + x(3 + -2i + x)) = y
((3 * 3 + -2i * 3 + x * 3) + 2i * (3 + -2i + x) + x(3 + -2i + x)) = y
((9 + -6i + 3x) + 2i * (3 + -2i + x) + x(3 + -2i + x)) = y
(9 + -6i + 3x + (3 * 2i + -2i * 2i + x * 2i) + x(3 + -2i + x)) = y

Reorder the terms:
(9 + -6i + 3x + (6i + 2ix + -4i2) + x(3 + -2i + x)) = y
(9 + -6i + 3x + (6i + 2ix + -4i2) + x(3 + -2i + x)) = y
(9 + -6i + 3x + 6i + 2ix + -4i2 + (3 * x + -2i * x + x * x)) = y

Reorder the terms:
(9 + -6i + 3x + 6i + 2ix + -4i2 + (-2ix + 3x + x2)) = y
(9 + -6i + 3x + 6i + 2ix + -4i2 + (-2ix + 3x + x2)) = y

Reorder the terms:
(9 + -6i + 6i + 2ix + -2ix + -4i2 + 3x + 3x + x2) = y

Combine like terms: -6i + 6i = 0
(9 + 0 + 2ix + -2ix + -4i2 + 3x + 3x + x2) = y
(9 + 2ix + -2ix + -4i2 + 3x + 3x + x2) = y

Combine like terms: 2ix + -2ix = 0
(9 + 0 + -4i2 + 3x + 3x + x2) = y
(9 + -4i2 + 3x + 3x + x2) = y

Combine like terms: 3x + 3x = 6x
(9 + -4i2 + 6x + x2) = y

Solving
9 + -4i2 + 6x + x2 = y

Solving for variable 'i'.

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

Add '-9' to each side of the equation.
9 + -4i2 + 6x + -9 + x2 = -9 + y

Reorder the terms:
9 + -9 + -4i2 + 6x + x2 = -9 + y

Combine like terms: 9 + -9 = 0
0 + -4i2 + 6x + x2 = -9 + y
-4i2 + 6x + x2 = -9 + y

Add '-6x' to each side of the equation.
-4i2 + 6x + -6x + x2 = -9 + -6x + y

Combine like terms: 6x + -6x = 0
-4i2 + 0 + x2 = -9 + -6x + y
-4i2 + x2 = -9 + -6x + y

Add '-1x2' to each side of the equation.
-4i2 + x2 + -1x2 = -9 + -6x + -1x2 + y

Combine like terms: x2 + -1x2 = 0
-4i2 + 0 = -9 + -6x + -1x2 + y
-4i2 = -9 + -6x + -1x2 + y

Divide each side by '-4'.
i2 = 2.25 + 1.5x + 0.25x2 + -0.25y

Simplifying
i2 = 2.25 + 1.5x + 0.25x2 + -0.25y

Reorder the terms:
-2.25 + i2 + -1.5x + -0.25x2 + 0.25y = 2.25 + 1.5x + 0.25x2 + -0.25y + -2.25 + -1.5x + -0.25x2 + 0.25y

Reorder the terms:
-2.25 + i2 + -1.5x + -0.25x2 + 0.25y = 2.25 + -2.25 + 1.5x + -1.5x + 0.25x2 + -0.25x2 + -0.25y + 0.25y

Combine like terms: 2.25 + -2.25 = 0.00
-2.25 + i2 + -1.5x + -0.25x2 + 0.25y = 0.00 + 1.5x + -1.5x + 0.25x2 + -0.25x2 + -0.25y + 0.25y
-2.25 + i2 + -1.5x + -0.25x2 + 0.25y = 1.5x + -1.5x + 0.25x2 + -0.25x2 + -0.25y + 0.25y

Combine like terms: 1.5x + -1.5x = 0.0
-2.25 + i2 + -1.5x + -0.25x2 + 0.25y = 0.0 + 0.25x2 + -0.25x2 + -0.25y + 0.25y
-2.25 + i2 + -1.5x + -0.25x2 + 0.25y = 0.25x2 + -0.25x2 + -0.25y + 0.25y

Combine like terms: 0.25x2 + -0.25x2 = 0.00
-2.25 + i2 + -1.5x + -0.25x2 + 0.25y = 0.00 + -0.25y + 0.25y
-2.25 + i2 + -1.5x + -0.25x2 + 0.25y = -0.25y + 0.25y

Combine like terms: -0.25y + 0.25y = 0.00
-2.25 + i2 + -1.5x + -0.25x2 + 0.25y = 0.00

The solution to this equation could not be determined.

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