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

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


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

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

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

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

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

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

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

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

Multiply (-16 + -4i + -1ix + x2) * (-4 + i + x)
(-16(-4 + i + x) + -4i * (-4 + i + x) + -1ix * (-4 + i + x) + x2(-4 + i + x)) = 0
((-4 * -16 + i * -16 + x * -16) + -4i * (-4 + i + x) + -1ix * (-4 + i + x) + x2(-4 + i + x)) = 0
((64 + -16i + -16x) + -4i * (-4 + i + x) + -1ix * (-4 + i + x) + x2(-4 + i + x)) = 0
(64 + -16i + -16x + (-4 * -4i + i * -4i + x * -4i) + -1ix * (-4 + i + x) + x2(-4 + i + x)) = 0

Reorder the terms:
(64 + -16i + -16x + (16i + -4ix + -4i2) + -1ix * (-4 + i + x) + x2(-4 + i + x)) = 0
(64 + -16i + -16x + (16i + -4ix + -4i2) + -1ix * (-4 + i + x) + x2(-4 + i + x)) = 0
(64 + -16i + -16x + 16i + -4ix + -4i2 + (-4 * -1ix + i * -1ix + x * -1ix) + x2(-4 + i + x)) = 0

Reorder the terms:
(64 + -16i + -16x + 16i + -4ix + -4i2 + (4ix + -1ix2 + -1i2x) + x2(-4 + i + x)) = 0
(64 + -16i + -16x + 16i + -4ix + -4i2 + (4ix + -1ix2 + -1i2x) + x2(-4 + i + x)) = 0
(64 + -16i + -16x + 16i + -4ix + -4i2 + 4ix + -1ix2 + -1i2x + (-4 * x2 + i * x2 + x * x2)) = 0

Reorder the terms:
(64 + -16i + -16x + 16i + -4ix + -4i2 + 4ix + -1ix2 + -1i2x + (ix2 + -4x2 + x3)) = 0
(64 + -16i + -16x + 16i + -4ix + -4i2 + 4ix + -1ix2 + -1i2x + (ix2 + -4x2 + x3)) = 0

Reorder the terms:
(64 + -16i + 16i + -4ix + 4ix + -1ix2 + ix2 + -4i2 + -1i2x + -16x + -4x2 + x3) = 0

Combine like terms: -16i + 16i = 0
(64 + 0 + -4ix + 4ix + -1ix2 + ix2 + -4i2 + -1i2x + -16x + -4x2 + x3) = 0
(64 + -4ix + 4ix + -1ix2 + ix2 + -4i2 + -1i2x + -16x + -4x2 + x3) = 0

Combine like terms: -4ix + 4ix = 0
(64 + 0 + -1ix2 + ix2 + -4i2 + -1i2x + -16x + -4x2 + x3) = 0
(64 + -1ix2 + ix2 + -4i2 + -1i2x + -16x + -4x2 + x3) = 0

Combine like terms: -1ix2 + ix2 = 0
(64 + 0 + -4i2 + -1i2x + -16x + -4x2 + x3) = 0
(64 + -4i2 + -1i2x + -16x + -4x2 + x3) = 0

Solving
64 + -4i2 + -1i2x + -16x + -4x2 + x3 = 0

Solving for variable 'i'.

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

Add '-64' to each side of the equation.
64 + -4i2 + -1i2x + -16x + -4x2 + -64 + x3 = 0 + -64

Reorder the terms:
64 + -64 + -4i2 + -1i2x + -16x + -4x2 + x3 = 0 + -64

Combine like terms: 64 + -64 = 0
0 + -4i2 + -1i2x + -16x + -4x2 + x3 = 0 + -64
-4i2 + -1i2x + -16x + -4x2 + x3 = 0 + -64

Combine like terms: 0 + -64 = -64
-4i2 + -1i2x + -16x + -4x2 + x3 = -64

Add '16x' to each side of the equation.
-4i2 + -1i2x + -16x + -4x2 + 16x + x3 = -64 + 16x

Reorder the terms:
-4i2 + -1i2x + -16x + 16x + -4x2 + x3 = -64 + 16x

Combine like terms: -16x + 16x = 0
-4i2 + -1i2x + 0 + -4x2 + x3 = -64 + 16x
-4i2 + -1i2x + -4x2 + x3 = -64 + 16x

Add '4x2' to each side of the equation.
-4i2 + -1i2x + -4x2 + 4x2 + x3 = -64 + 16x + 4x2

Combine like terms: -4x2 + 4x2 = 0
-4i2 + -1i2x + 0 + x3 = -64 + 16x + 4x2
-4i2 + -1i2x + x3 = -64 + 16x + 4x2

Add '-1x3' to each side of the equation.
-4i2 + -1i2x + x3 + -1x3 = -64 + 16x + 4x2 + -1x3

Combine like terms: x3 + -1x3 = 0
-4i2 + -1i2x + 0 = -64 + 16x + 4x2 + -1x3
-4i2 + -1i2x = -64 + 16x + 4x2 + -1x3

Reorder the terms:
64 + -4i2 + -1i2x + -16x + -4x2 + x3 = -64 + 16x + 4x2 + -1x3 + 64 + -16x + -4x2 + x3

Reorder the terms:
64 + -4i2 + -1i2x + -16x + -4x2 + x3 = -64 + 64 + 16x + -16x + 4x2 + -4x2 + -1x3 + x3

Combine like terms: -64 + 64 = 0
64 + -4i2 + -1i2x + -16x + -4x2 + x3 = 0 + 16x + -16x + 4x2 + -4x2 + -1x3 + x3
64 + -4i2 + -1i2x + -16x + -4x2 + x3 = 16x + -16x + 4x2 + -4x2 + -1x3 + x3

Combine like terms: 16x + -16x = 0
64 + -4i2 + -1i2x + -16x + -4x2 + x3 = 0 + 4x2 + -4x2 + -1x3 + x3
64 + -4i2 + -1i2x + -16x + -4x2 + x3 = 4x2 + -4x2 + -1x3 + x3

Combine like terms: 4x2 + -4x2 = 0
64 + -4i2 + -1i2x + -16x + -4x2 + x3 = 0 + -1x3 + x3
64 + -4i2 + -1i2x + -16x + -4x2 + x3 = -1x3 + x3

Combine like terms: -1x3 + x3 = 0
64 + -4i2 + -1i2x + -16x + -4x2 + x3 = 0

The solution to this equation could not be determined.

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