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

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


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

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

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

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

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

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

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

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

Combine like terms: 1ix + -1ix = 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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