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

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


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

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

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

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

Multiply (-3 + -1i + x) * (-3 + 1i + x)
(-3(-3 + 1i + x) + -1i * (-3 + 1i + x) + x(-3 + 1i + x))(-4 + x) = 0
((-3 * -3 + 1i * -3 + x * -3) + -1i * (-3 + 1i + x) + x(-3 + 1i + x))(-4 + x) = 0
((9 + -3i + -3x) + -1i * (-3 + 1i + x) + x(-3 + 1i + x))(-4 + x) = 0
(9 + -3i + -3x + (-3 * -1i + 1i * -1i + x * -1i) + x(-3 + 1i + x))(-4 + x) = 0

Reorder the terms:
(9 + -3i + -3x + (3i + -1ix + -1i2) + x(-3 + 1i + x))(-4 + x) = 0
(9 + -3i + -3x + (3i + -1ix + -1i2) + x(-3 + 1i + x))(-4 + x) = 0
(9 + -3i + -3x + 3i + -1ix + -1i2 + (-3 * x + 1i * x + x * x))(-4 + x) = 0

Reorder the terms:
(9 + -3i + -3x + 3i + -1ix + -1i2 + (1ix + -3x + x2))(-4 + x) = 0
(9 + -3i + -3x + 3i + -1ix + -1i2 + (1ix + -3x + x2))(-4 + x) = 0

Reorder the terms:
(9 + -3i + 3i + -1ix + 1ix + -1i2 + -3x + -3x + x2)(-4 + x) = 0

Combine like terms: -3i + 3i = 0
(9 + 0 + -1ix + 1ix + -1i2 + -3x + -3x + x2)(-4 + x) = 0
(9 + -1ix + 1ix + -1i2 + -3x + -3x + x2)(-4 + x) = 0

Combine like terms: -1ix + 1ix = 0
(9 + 0 + -1i2 + -3x + -3x + x2)(-4 + x) = 0
(9 + -1i2 + -3x + -3x + x2)(-4 + x) = 0

Combine like terms: -3x + -3x = -6x
(9 + -1i2 + -6x + x2)(-4 + x) = 0

Multiply (9 + -1i2 + -6x + x2) * (-4 + x)
(9(-4 + x) + -1i2 * (-4 + x) + -6x * (-4 + x) + x2(-4 + x)) = 0
((-4 * 9 + x * 9) + -1i2 * (-4 + x) + -6x * (-4 + x) + x2(-4 + x)) = 0
((-36 + 9x) + -1i2 * (-4 + x) + -6x * (-4 + x) + x2(-4 + x)) = 0
(-36 + 9x + (-4 * -1i2 + x * -1i2) + -6x * (-4 + x) + x2(-4 + x)) = 0
(-36 + 9x + (4i2 + -1i2x) + -6x * (-4 + x) + x2(-4 + x)) = 0
(-36 + 9x + 4i2 + -1i2x + (-4 * -6x + x * -6x) + x2(-4 + x)) = 0
(-36 + 9x + 4i2 + -1i2x + (24x + -6x2) + x2(-4 + x)) = 0
(-36 + 9x + 4i2 + -1i2x + 24x + -6x2 + (-4 * x2 + x * x2)) = 0
(-36 + 9x + 4i2 + -1i2x + 24x + -6x2 + (-4x2 + x3)) = 0

Reorder the terms:
(-36 + 4i2 + -1i2x + 9x + 24x + -6x2 + -4x2 + x3) = 0

Combine like terms: 9x + 24x = 33x
(-36 + 4i2 + -1i2x + 33x + -6x2 + -4x2 + x3) = 0

Combine like terms: -6x2 + -4x2 = -10x2
(-36 + 4i2 + -1i2x + 33x + -10x2 + x3) = 0

Solving
-36 + 4i2 + -1i2x + 33x + -10x2 + x3 = 0

Solving for variable 'i'.

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

Add '36' to each side of the equation.
-36 + 4i2 + -1i2x + 33x + -10x2 + 36 + x3 = 0 + 36

Reorder the terms:
-36 + 36 + 4i2 + -1i2x + 33x + -10x2 + x3 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + 4i2 + -1i2x + 33x + -10x2 + x3 = 0 + 36
4i2 + -1i2x + 33x + -10x2 + x3 = 0 + 36

Combine like terms: 0 + 36 = 36
4i2 + -1i2x + 33x + -10x2 + x3 = 36

Add '-33x' to each side of the equation.
4i2 + -1i2x + 33x + -10x2 + -33x + x3 = 36 + -33x

Reorder the terms:
4i2 + -1i2x + 33x + -33x + -10x2 + x3 = 36 + -33x

Combine like terms: 33x + -33x = 0
4i2 + -1i2x + 0 + -10x2 + x3 = 36 + -33x
4i2 + -1i2x + -10x2 + x3 = 36 + -33x

Add '10x2' to each side of the equation.
4i2 + -1i2x + -10x2 + 10x2 + x3 = 36 + -33x + 10x2

Combine like terms: -10x2 + 10x2 = 0
4i2 + -1i2x + 0 + x3 = 36 + -33x + 10x2
4i2 + -1i2x + x3 = 36 + -33x + 10x2

Add '-1x3' to each side of the equation.
4i2 + -1i2x + x3 + -1x3 = 36 + -33x + 10x2 + -1x3

Combine like terms: x3 + -1x3 = 0
4i2 + -1i2x + 0 = 36 + -33x + 10x2 + -1x3
4i2 + -1i2x = 36 + -33x + 10x2 + -1x3

Reorder the terms:
-36 + 4i2 + -1i2x + 33x + -10x2 + x3 = 36 + -33x + 10x2 + -1x3 + -36 + 33x + -10x2 + x3

Reorder the terms:
-36 + 4i2 + -1i2x + 33x + -10x2 + x3 = 36 + -36 + -33x + 33x + 10x2 + -10x2 + -1x3 + x3

Combine like terms: 36 + -36 = 0
-36 + 4i2 + -1i2x + 33x + -10x2 + x3 = 0 + -33x + 33x + 10x2 + -10x2 + -1x3 + x3
-36 + 4i2 + -1i2x + 33x + -10x2 + x3 = -33x + 33x + 10x2 + -10x2 + -1x3 + x3

Combine like terms: -33x + 33x = 0
-36 + 4i2 + -1i2x + 33x + -10x2 + x3 = 0 + 10x2 + -10x2 + -1x3 + x3
-36 + 4i2 + -1i2x + 33x + -10x2 + x3 = 10x2 + -10x2 + -1x3 + x3

Combine like terms: 10x2 + -10x2 = 0
-36 + 4i2 + -1i2x + 33x + -10x2 + x3 = 0 + -1x3 + x3
-36 + 4i2 + -1i2x + 33x + -10x2 + x3 = -1x3 + x3

Combine like terms: -1x3 + x3 = 0
-36 + 4i2 + -1i2x + 33x + -10x2 + x3 = 0

The solution to this equation could not be determined.

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