(x-4+2i)(x-4-2i)=0

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Solution for (x-4+2i)(x-4-2i)=0 equation: 


Simplifying
(x + -4 + 2i)(x + -4 + -2i) = 0

Reorder the terms:
(-4 + 2i + x)(x + -4 + -2i) = 0

Reorder the terms:
(-4 + 2i + x)(-4 + -2i + x) = 0

Multiply (-4 + 2i + x) * (-4 + -2i + x)
(-4(-4 + -2i + x) + 2i * (-4 + -2i + x) + x(-4 + -2i + x)) = 0
((-4 * -4 + -2i * -4 + x * -4) + 2i * (-4 + -2i + x) + x(-4 + -2i + x)) = 0
((16 + 8i + -4x) + 2i * (-4 + -2i + x) + x(-4 + -2i + x)) = 0
(16 + 8i + -4x + (-4 * 2i + -2i * 2i + x * 2i) + x(-4 + -2i + x)) = 0

Reorder the terms:
(16 + 8i + -4x + (-8i + 2ix + -4i2) + x(-4 + -2i + x)) = 0
(16 + 8i + -4x + (-8i + 2ix + -4i2) + x(-4 + -2i + x)) = 0
(16 + 8i + -4x + -8i + 2ix + -4i2 + (-4 * x + -2i * x + x * x)) = 0

Reorder the terms:
(16 + 8i + -4x + -8i + 2ix + -4i2 + (-2ix + -4x + x2)) = 0
(16 + 8i + -4x + -8i + 2ix + -4i2 + (-2ix + -4x + x2)) = 0

Reorder the terms:
(16 + 8i + -8i + 2ix + -2ix + -4i2 + -4x + -4x + x2) = 0

Combine like terms: 8i + -8i = 0
(16 + 0 + 2ix + -2ix + -4i2 + -4x + -4x + x2) = 0
(16 + 2ix + -2ix + -4i2 + -4x + -4x + x2) = 0

Combine like terms: 2ix + -2ix = 0
(16 + 0 + -4i2 + -4x + -4x + x2) = 0
(16 + -4i2 + -4x + -4x + x2) = 0

Combine like terms: -4x + -4x = -8x
(16 + -4i2 + -8x + x2) = 0

Solving
16 + -4i2 + -8x + x2 = 0

Solving for variable 'i'.

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

Add '-16' to each side of the equation.
16 + -4i2 + -8x + -16 + x2 = 0 + -16

Reorder the terms:
16 + -16 + -4i2 + -8x + x2 = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -4i2 + -8x + x2 = 0 + -16
-4i2 + -8x + x2 = 0 + -16

Combine like terms: 0 + -16 = -16
-4i2 + -8x + x2 = -16

Add '8x' to each side of the equation.
-4i2 + -8x + 8x + x2 = -16 + 8x

Combine like terms: -8x + 8x = 0
-4i2 + 0 + x2 = -16 + 8x
-4i2 + x2 = -16 + 8x

Add '-1x2' to each side of the equation.
-4i2 + x2 + -1x2 = -16 + 8x + -1x2

Combine like terms: x2 + -1x2 = 0
-4i2 + 0 = -16 + 8x + -1x2
-4i2 = -16 + 8x + -1x2

Divide each side by '-4'.
i2 = 4 + -2x + 0.25x2

Simplifying
i2 = 4 + -2x + 0.25x2

Reorder the terms:
-4 + i2 + 2x + -0.25x2 = 4 + -2x + 0.25x2 + -4 + 2x + -0.25x2

Reorder the terms:
-4 + i2 + 2x + -0.25x2 = 4 + -4 + -2x + 2x + 0.25x2 + -0.25x2

Combine like terms: 4 + -4 = 0
-4 + i2 + 2x + -0.25x2 = 0 + -2x + 2x + 0.25x2 + -0.25x2
-4 + i2 + 2x + -0.25x2 = -2x + 2x + 0.25x2 + -0.25x2

Combine like terms: -2x + 2x = 0
-4 + i2 + 2x + -0.25x2 = 0 + 0.25x2 + -0.25x2
-4 + i2 + 2x + -0.25x2 = 0.25x2 + -0.25x2

Combine like terms: 0.25x2 + -0.25x2 = 0.00
-4 + i2 + 2x + -0.25x2 = 0.00

The solution to this equation could not be determined.

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