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

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


Simplifying
(x + -4 + -1i)(x + -4 + i) = 0

Reorder the terms:
(-4 + -1i + x)(x + -4 + i) = 0

Reorder the terms:
(-4 + -1i + x)(-4 + i + x) = 0

Multiply (-4 + -1i + x) * (-4 + i + x)
(-4(-4 + i + x) + -1i * (-4 + i + x) + x(-4 + i + x)) = 0
((-4 * -4 + i * -4 + x * -4) + -1i * (-4 + i + x) + x(-4 + i + x)) = 0
((16 + -4i + -4x) + -1i * (-4 + i + x) + x(-4 + i + x)) = 0
(16 + -4i + -4x + (-4 * -1i + i * -1i + x * -1i) + x(-4 + i + x)) = 0

Reorder the terms:
(16 + -4i + -4x + (4i + -1ix + -1i2) + x(-4 + i + x)) = 0
(16 + -4i + -4x + (4i + -1ix + -1i2) + x(-4 + i + x)) = 0
(16 + -4i + -4x + 4i + -1ix + -1i2 + (-4 * x + i * x + x * x)) = 0

Reorder the terms:
(16 + -4i + -4x + 4i + -1ix + -1i2 + (ix + -4x + x2)) = 0
(16 + -4i + -4x + 4i + -1ix + -1i2 + (ix + -4x + x2)) = 0

Reorder the terms:
(16 + -4i + 4i + -1ix + ix + -1i2 + -4x + -4x + x2) = 0

Combine like terms: -4i + 4i = 0
(16 + 0 + -1ix + ix + -1i2 + -4x + -4x + x2) = 0
(16 + -1ix + ix + -1i2 + -4x + -4x + x2) = 0

Combine like terms: -1ix + ix = 0
(16 + 0 + -1i2 + -4x + -4x + x2) = 0
(16 + -1i2 + -4x + -4x + x2) = 0

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

Solving
16 + -1i2 + -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 + -1i2 + -8x + -16 + x2 = 0 + -16

Reorder the terms:
16 + -16 + -1i2 + -8x + x2 = 0 + -16

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

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

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

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

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

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

Divide each side by '-1'.
i2 = 16 + -8x + x2

Simplifying
i2 = 16 + -8x + x2

Reorder the terms:
-16 + i2 + 8x + -1x2 = 16 + -8x + x2 + -16 + 8x + -1x2

Reorder the terms:
-16 + i2 + 8x + -1x2 = 16 + -16 + -8x + 8x + x2 + -1x2

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

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

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

The solution to this equation could not be determined.

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