[x-(3+4i)][x-(3-4i)]=0

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Solution for [x-(3+4i)][x-(3-4i)]=0 equation: 


Simplifying
[x + -1(3 + 4i)][x + -1(3 + -4i)] = 0
[x + (3 * -1 + 4i * -1)][x + -1(3 + -4i)] = 0
[x + (-3 + -4i)][x + -1(3 + -4i)] = 0

Reorder the terms:
[-3 + -4i + x][x + -1(3 + -4i)] = 0
[-3 + -4i + x][x + (3 * -1 + -4i * -1)] = 0
[-3 + -4i + x][x + (-3 + 4i)] = 0

Reorder the terms:
[-3 + -4i + x][-3 + 4i + x] = 0

Multiply [-3 + -4i + x] * [-3 + 4i + x]
[-3[-3 + 4i + x] + -4i * [-3 + 4i + x] + x[-3 + 4i + x]] = 0
[[-3 * -3 + 4i * -3 + x * -3] + -4i * [-3 + 4i + x] + x[-3 + 4i + x]] = 0
[[9 + -12i + -3x] + -4i * [-3 + 4i + x] + x[-3 + 4i + x]] = 0
[9 + -12i + -3x + [-3 * -4i + 4i * -4i + x * -4i] + x[-3 + 4i + x]] = 0

Reorder the terms:
[9 + -12i + -3x + [12i + -4ix + -16i2] + x[-3 + 4i + x]] = 0
[9 + -12i + -3x + [12i + -4ix + -16i2] + x[-3 + 4i + x]] = 0
[9 + -12i + -3x + 12i + -4ix + -16i2 + [-3 * x + 4i * x + x * x]] = 0

Reorder the terms:
[9 + -12i + -3x + 12i + -4ix + -16i2 + [4ix + -3x + x2]] = 0
[9 + -12i + -3x + 12i + -4ix + -16i2 + [4ix + -3x + x2]] = 0

Reorder the terms:
[9 + -12i + 12i + -4ix + 4ix + -16i2 + -3x + -3x + x2] = 0

Combine like terms: -12i + 12i = 0
[9 + 0 + -4ix + 4ix + -16i2 + -3x + -3x + x2] = 0
[9 + -4ix + 4ix + -16i2 + -3x + -3x + x2] = 0

Combine like terms: -4ix + 4ix = 0
[9 + 0 + -16i2 + -3x + -3x + x2] = 0
[9 + -16i2 + -3x + -3x + x2] = 0

Combine like terms: -3x + -3x = -6x
[9 + -16i2 + -6x + x2] = 0

Solving
9 + -16i2 + -6x + x2 = 0

Solving for variable 'i'.

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

Add '-9' to each side of the equation.
9 + -16i2 + -6x + -9 + x2 = 0 + -9

Reorder the terms:
9 + -9 + -16i2 + -6x + x2 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -16i2 + -6x + x2 = 0 + -9
-16i2 + -6x + x2 = 0 + -9

Combine like terms: 0 + -9 = -9
-16i2 + -6x + x2 = -9

Add '6x' to each side of the equation.
-16i2 + -6x + 6x + x2 = -9 + 6x

Combine like terms: -6x + 6x = 0
-16i2 + 0 + x2 = -9 + 6x
-16i2 + x2 = -9 + 6x

Add '-1x2' to each side of the equation.
-16i2 + x2 + -1x2 = -9 + 6x + -1x2

Combine like terms: x2 + -1x2 = 0
-16i2 + 0 = -9 + 6x + -1x2
-16i2 = -9 + 6x + -1x2

Divide each side by '-16'.
i2 = 0.5625 + -0.375x + 0.0625x2

Simplifying
i2 = 0.5625 + -0.375x + 0.0625x2

Reorder the terms:
-0.5625 + i2 + 0.375x + -0.0625x2 = 0.5625 + -0.375x + 0.0625x2 + -0.5625 + 0.375x + -0.0625x2

Reorder the terms:
-0.5625 + i2 + 0.375x + -0.0625x2 = 0.5625 + -0.5625 + -0.375x + 0.375x + 0.0625x2 + -0.0625x2

Combine like terms: 0.5625 + -0.5625 = 0.0000
-0.5625 + i2 + 0.375x + -0.0625x2 = 0.0000 + -0.375x + 0.375x + 0.0625x2 + -0.0625x2
-0.5625 + i2 + 0.375x + -0.0625x2 = -0.375x + 0.375x + 0.0625x2 + -0.0625x2

Combine like terms: -0.375x + 0.375x = 0.000
-0.5625 + i2 + 0.375x + -0.0625x2 = 0.000 + 0.0625x2 + -0.0625x2
-0.5625 + i2 + 0.375x + -0.0625x2 = 0.0625x2 + -0.0625x2

Combine like terms: 0.0625x2 + -0.0625x2 = 0.0000
-0.5625 + i2 + 0.375x + -0.0625x2 = 0.0000

The solution to this equation could not be determined.

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