(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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