(x-3+2i)(x-3-2i)=0

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Solution for (x-3+2i)(x-3-2i)=0 equation: 


Simplifying
(x + -3 + 2i)(x + -3 + -2i) = 0

Reorder the terms:
(-3 + 2i + x)(x + -3 + -2i) = 0

Reorder the terms:
(-3 + 2i + x)(-3 + -2i + x) = 0

Multiply (-3 + 2i + x) * (-3 + -2i + x)
(-3(-3 + -2i + x) + 2i * (-3 + -2i + x) + x(-3 + -2i + x)) = 0
((-3 * -3 + -2i * -3 + x * -3) + 2i * (-3 + -2i + x) + x(-3 + -2i + x)) = 0
((9 + 6i + -3x) + 2i * (-3 + -2i + x) + x(-3 + -2i + x)) = 0
(9 + 6i + -3x + (-3 * 2i + -2i * 2i + x * 2i) + x(-3 + -2i + x)) = 0

Reorder the terms:
(9 + 6i + -3x + (-6i + 2ix + -4i2) + x(-3 + -2i + x)) = 0
(9 + 6i + -3x + (-6i + 2ix + -4i2) + x(-3 + -2i + x)) = 0
(9 + 6i + -3x + -6i + 2ix + -4i2 + (-3 * x + -2i * x + x * x)) = 0

Reorder the terms:
(9 + 6i + -3x + -6i + 2ix + -4i2 + (-2ix + -3x + x2)) = 0
(9 + 6i + -3x + -6i + 2ix + -4i2 + (-2ix + -3x + x2)) = 0

Reorder the terms:
(9 + 6i + -6i + 2ix + -2ix + -4i2 + -3x + -3x + x2) = 0

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

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

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

Solving
9 + -4i2 + -6x + x2 = 0

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 = 0 + -9

Reorder the terms:
9 + -9 + -4i2 + -6x + x2 = 0 + -9

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

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

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

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

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

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

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

Simplifying
i2 = 2.25 + -1.5x + 0.25x2

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

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

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

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

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

The solution to this equation could not be determined.

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