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

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


Simplifying
(x + -3 + i)(x + -3 + -1i) = y

Reorder the terms:
(-3 + i + x)(x + -3 + -1i) = y

Reorder the terms:
(-3 + i + x)(-3 + -1i + x) = y

Multiply (-3 + i + x) * (-3 + -1i + x)
(-3(-3 + -1i + x) + i(-3 + -1i + x) + x(-3 + -1i + x)) = y
((-3 * -3 + -1i * -3 + x * -3) + i(-3 + -1i + x) + x(-3 + -1i + x)) = y
((9 + 3i + -3x) + i(-3 + -1i + x) + x(-3 + -1i + x)) = y
(9 + 3i + -3x + (-3 * i + -1i * i + x * i) + x(-3 + -1i + x)) = y

Reorder the terms:
(9 + 3i + -3x + (-3i + ix + -1i2) + x(-3 + -1i + x)) = y
(9 + 3i + -3x + (-3i + ix + -1i2) + x(-3 + -1i + x)) = y
(9 + 3i + -3x + -3i + ix + -1i2 + (-3 * x + -1i * x + x * x)) = y

Reorder the terms:
(9 + 3i + -3x + -3i + ix + -1i2 + (-1ix + -3x + x2)) = y
(9 + 3i + -3x + -3i + ix + -1i2 + (-1ix + -3x + x2)) = y

Reorder the terms:
(9 + 3i + -3i + ix + -1ix + -1i2 + -3x + -3x + x2) = y

Combine like terms: 3i + -3i = 0
(9 + 0 + ix + -1ix + -1i2 + -3x + -3x + x2) = y
(9 + ix + -1ix + -1i2 + -3x + -3x + x2) = y

Combine like terms: ix + -1ix = 0
(9 + 0 + -1i2 + -3x + -3x + x2) = y
(9 + -1i2 + -3x + -3x + x2) = y

Combine like terms: -3x + -3x = -6x
(9 + -1i2 + -6x + x2) = y

Solving
9 + -1i2 + -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 + -1i2 + -6x + -9 + x2 = -9 + y

Reorder the terms:
9 + -9 + -1i2 + -6x + x2 = -9 + y

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

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

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

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

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

Divide each side by '-1'.
i2 = 9 + -6x + x2 + -1y

Simplifying
i2 = 9 + -6x + x2 + -1y

Reorder the terms:
-9 + i2 + 6x + -1x2 + y = 9 + -6x + x2 + -1y + -9 + 6x + -1x2 + y

Reorder the terms:
-9 + i2 + 6x + -1x2 + y = 9 + -9 + -6x + 6x + x2 + -1x2 + -1y + y

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

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

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

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

The solution to this equation could not be determined.

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