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

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


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

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

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

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

Reorder the terms:
(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)) = 0

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

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

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

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

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

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

Solving for variable 'i'.

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

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

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

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

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

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

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

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

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

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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