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

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


Simplifying
[x + -1(-4 + 2i)][x + -1(-4 + -2i)] = 0
[x + (-4 * -1 + 2i * -1)][x + -1(-4 + -2i)] = 0
[x + (4 + -2i)][x + -1(-4 + -2i)] = 0

Reorder the terms:
[4 + -2i + x][x + -1(-4 + -2i)] = 0
[4 + -2i + x][x + (-4 * -1 + -2i * -1)] = 0
[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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