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

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


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

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

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

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

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

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

Combine like terms: -4x + -4x = -8x
(16 + -4I + 4i + -1iI + -1ix + -8x + xI + x2) = 0

Solving
16 + -4I + 4i + -1iI + -1ix + -8x + xI + 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 + -4I + 4i + -1iI + -1ix + -8x + xI + -16 + x2 = 0 + -16

Reorder the terms:
16 + -16 + -4I + 4i + -1iI + -1ix + -8x + xI + x2 = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -4I + 4i + -1iI + -1ix + -8x + xI + x2 = 0 + -16
-4I + 4i + -1iI + -1ix + -8x + xI + x2 = 0 + -16

Combine like terms: 0 + -16 = -16
-4I + 4i + -1iI + -1ix + -8x + xI + x2 = -16

Add '-4i' to each side of the equation.
-4I + 4i + -1iI + -1ix + -8x + xI + -4i + x2 = -16 + -4i

Reorder the terms:
-4I + 4i + -4i + -1iI + -1ix + -8x + xI + x2 = -16 + -4i

Combine like terms: 4i + -4i = 0
-4I + 0 + -1iI + -1ix + -8x + xI + x2 = -16 + -4i
-4I + -1iI + -1ix + -8x + xI + x2 = -16 + -4i

Add 'ix' to each side of the equation.
-4I + -1iI + -1ix + -8x + xI + ix + x2 = -16 + -4i + ix

Reorder the terms:
-4I + -1iI + -1ix + ix + -8x + xI + x2 = -16 + -4i + ix

Combine like terms: -1ix + ix = 0
-4I + -1iI + 0 + -8x + xI + x2 = -16 + -4i + ix
-4I + -1iI + -8x + xI + x2 = -16 + -4i + ix

Add '8x' to each side of the equation.
-4I + -1iI + -8x + xI + 8x + x2 = -16 + -4i + ix + 8x

Reorder the terms:
-4I + -1iI + -8x + 8x + xI + x2 = -16 + -4i + ix + 8x

Combine like terms: -8x + 8x = 0
-4I + -1iI + 0 + xI + x2 = -16 + -4i + ix + 8x
-4I + -1iI + xI + x2 = -16 + -4i + ix + 8x

Add '-1x2' to each side of the equation.
-4I + -1iI + xI + x2 + -1x2 = -16 + -4i + ix + 8x + -1x2

Combine like terms: x2 + -1x2 = 0
-4I + -1iI + xI + 0 = -16 + -4i + ix + 8x + -1x2
-4I + -1iI + xI = -16 + -4i + ix + 8x + -1x2

Reorder the terms:
16 + -4I + 4i + -1iI + -1ix + -8x + xI + x2 = -16 + -4i + ix + 8x + -1x2 + 16 + 4i + -1ix + -8x + x2

Reorder the terms:
16 + -4I + 4i + -1iI + -1ix + -8x + xI + x2 = -16 + 16 + -4i + 4i + ix + -1ix + 8x + -8x + -1x2 + x2

Combine like terms: -16 + 16 = 0
16 + -4I + 4i + -1iI + -1ix + -8x + xI + x2 = 0 + -4i + 4i + ix + -1ix + 8x + -8x + -1x2 + x2
16 + -4I + 4i + -1iI + -1ix + -8x + xI + x2 = -4i + 4i + ix + -1ix + 8x + -8x + -1x2 + x2

Combine like terms: -4i + 4i = 0
16 + -4I + 4i + -1iI + -1ix + -8x + xI + x2 = 0 + ix + -1ix + 8x + -8x + -1x2 + x2
16 + -4I + 4i + -1iI + -1ix + -8x + xI + x2 = ix + -1ix + 8x + -8x + -1x2 + x2

Combine like terms: ix + -1ix = 0
16 + -4I + 4i + -1iI + -1ix + -8x + xI + x2 = 0 + 8x + -8x + -1x2 + x2
16 + -4I + 4i + -1iI + -1ix + -8x + xI + x2 = 8x + -8x + -1x2 + x2

Combine like terms: 8x + -8x = 0
16 + -4I + 4i + -1iI + -1ix + -8x + xI + x2 = 0 + -1x2 + x2
16 + -4I + 4i + -1iI + -1ix + -8x + xI + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
16 + -4I + 4i + -1iI + -1ix + -8x + xI + x2 = 0

The solution to this equation could not be determined.

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