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

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


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

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

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

Multiply (-2 + -3i + x) * (-2 + 3i + x)
0 = (-2(-2 + 3i + x) + -3i * (-2 + 3i + x) + x(-2 + 3i + x))
0 = ((-2 * -2 + 3i * -2 + x * -2) + -3i * (-2 + 3i + x) + x(-2 + 3i + x))
0 = ((4 + -6i + -2x) + -3i * (-2 + 3i + x) + x(-2 + 3i + x))
0 = (4 + -6i + -2x + (-2 * -3i + 3i * -3i + x * -3i) + x(-2 + 3i + x))

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

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

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

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

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

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

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

Solving for variable 'i'.

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

Add '9i2' to each side of the equation.
0 + 9i2 = 4 + -9i2 + -4x + 9i2 + x2
Remove the zero:
9i2 = 4 + -9i2 + -4x + 9i2 + x2

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

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

Divide each side by '9'.
i2 = 0.4444444444 + -0.4444444444x + 0.1111111111x2

Simplifying
i2 = 0.4444444444 + -0.4444444444x + 0.1111111111x2

Reorder the terms:
-0.4444444444 + i2 + 0.4444444444x + -0.1111111111x2 = 0.4444444444 + -0.4444444444x + 0.1111111111x2 + -0.4444444444 + 0.4444444444x + -0.1111111111x2

Reorder the terms:
-0.4444444444 + i2 + 0.4444444444x + -0.1111111111x2 = 0.4444444444 + -0.4444444444 + -0.4444444444x + 0.4444444444x + 0.1111111111x2 + -0.1111111111x2

Combine like terms: 0.4444444444 + -0.4444444444 = 0.0000000000
-0.4444444444 + i2 + 0.4444444444x + -0.1111111111x2 = 0.0000000000 + -0.4444444444x + 0.4444444444x + 0.1111111111x2 + -0.1111111111x2
-0.4444444444 + i2 + 0.4444444444x + -0.1111111111x2 = -0.4444444444x + 0.4444444444x + 0.1111111111x2 + -0.1111111111x2

Combine like terms: -0.4444444444x + 0.4444444444x = 0.0000000000
-0.4444444444 + i2 + 0.4444444444x + -0.1111111111x2 = 0.0000000000 + 0.1111111111x2 + -0.1111111111x2
-0.4444444444 + i2 + 0.4444444444x + -0.1111111111x2 = 0.1111111111x2 + -0.1111111111x2

Combine like terms: 0.1111111111x2 + -0.1111111111x2 = 0.0000000000
-0.4444444444 + i2 + 0.4444444444x + -0.1111111111x2 = 0.0000000000

The solution to this equation could not be determined.

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