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

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


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

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

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

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

Multiply (-3 + x) * (-4 + i + x)
(-3(-4 + i + x) + x(-4 + i + x))(-4 + -1i + x) = 0
((-4 * -3 + i * -3 + x * -3) + x(-4 + i + x))(-4 + -1i + x) = 0
((12 + -3i + -3x) + x(-4 + i + x))(-4 + -1i + x) = 0
(12 + -3i + -3x + (-4 * x + i * x + x * x))(-4 + -1i + x) = 0

Reorder the terms:
(12 + -3i + -3x + (ix + -4x + x2))(-4 + -1i + x) = 0
(12 + -3i + -3x + (ix + -4x + x2))(-4 + -1i + x) = 0

Reorder the terms:
(12 + -3i + ix + -3x + -4x + x2)(-4 + -1i + x) = 0

Combine like terms: -3x + -4x = -7x
(12 + -3i + ix + -7x + x2)(-4 + -1i + x) = 0

Multiply (12 + -3i + ix + -7x + x2) * (-4 + -1i + x)
(12(-4 + -1i + x) + -3i * (-4 + -1i + x) + ix(-4 + -1i + x) + -7x * (-4 + -1i + x) + x2(-4 + -1i + x)) = 0
((-4 * 12 + -1i * 12 + x * 12) + -3i * (-4 + -1i + x) + ix(-4 + -1i + x) + -7x * (-4 + -1i + x) + x2(-4 + -1i + x)) = 0
((-48 + -12i + 12x) + -3i * (-4 + -1i + x) + ix(-4 + -1i + x) + -7x * (-4 + -1i + x) + x2(-4 + -1i + x)) = 0
(-48 + -12i + 12x + (-4 * -3i + -1i * -3i + x * -3i) + ix(-4 + -1i + x) + -7x * (-4 + -1i + x) + x2(-4 + -1i + x)) = 0

Reorder the terms:
(-48 + -12i + 12x + (12i + -3ix + 3i2) + ix(-4 + -1i + x) + -7x * (-4 + -1i + x) + x2(-4 + -1i + x)) = 0
(-48 + -12i + 12x + (12i + -3ix + 3i2) + ix(-4 + -1i + x) + -7x * (-4 + -1i + x) + x2(-4 + -1i + x)) = 0
(-48 + -12i + 12x + 12i + -3ix + 3i2 + (-4 * ix + -1i * ix + x * ix) + -7x * (-4 + -1i + x) + x2(-4 + -1i + x)) = 0

Reorder the terms:
(-48 + -12i + 12x + 12i + -3ix + 3i2 + (-4ix + ix2 + -1i2x) + -7x * (-4 + -1i + x) + x2(-4 + -1i + x)) = 0
(-48 + -12i + 12x + 12i + -3ix + 3i2 + (-4ix + ix2 + -1i2x) + -7x * (-4 + -1i + x) + x2(-4 + -1i + x)) = 0
(-48 + -12i + 12x + 12i + -3ix + 3i2 + -4ix + ix2 + -1i2x + (-4 * -7x + -1i * -7x + x * -7x) + x2(-4 + -1i + x)) = 0

Reorder the terms:
(-48 + -12i + 12x + 12i + -3ix + 3i2 + -4ix + ix2 + -1i2x + (7ix + 28x + -7x2) + x2(-4 + -1i + x)) = 0
(-48 + -12i + 12x + 12i + -3ix + 3i2 + -4ix + ix2 + -1i2x + (7ix + 28x + -7x2) + x2(-4 + -1i + x)) = 0
(-48 + -12i + 12x + 12i + -3ix + 3i2 + -4ix + ix2 + -1i2x + 7ix + 28x + -7x2 + (-4 * x2 + -1i * x2 + x * x2)) = 0

Reorder the terms:
(-48 + -12i + 12x + 12i + -3ix + 3i2 + -4ix + ix2 + -1i2x + 7ix + 28x + -7x2 + (-1ix2 + -4x2 + x3)) = 0
(-48 + -12i + 12x + 12i + -3ix + 3i2 + -4ix + ix2 + -1i2x + 7ix + 28x + -7x2 + (-1ix2 + -4x2 + x3)) = 0

Reorder the terms:
(-48 + -12i + 12i + -3ix + -4ix + 7ix + ix2 + -1ix2 + 3i2 + -1i2x + 12x + 28x + -7x2 + -4x2 + x3) = 0

Combine like terms: -12i + 12i = 0
(-48 + 0 + -3ix + -4ix + 7ix + ix2 + -1ix2 + 3i2 + -1i2x + 12x + 28x + -7x2 + -4x2 + x3) = 0
(-48 + -3ix + -4ix + 7ix + ix2 + -1ix2 + 3i2 + -1i2x + 12x + 28x + -7x2 + -4x2 + x3) = 0

Combine like terms: -3ix + -4ix = -7ix
(-48 + -7ix + 7ix + ix2 + -1ix2 + 3i2 + -1i2x + 12x + 28x + -7x2 + -4x2 + x3) = 0

Combine like terms: -7ix + 7ix = 0
(-48 + 0 + ix2 + -1ix2 + 3i2 + -1i2x + 12x + 28x + -7x2 + -4x2 + x3) = 0
(-48 + ix2 + -1ix2 + 3i2 + -1i2x + 12x + 28x + -7x2 + -4x2 + x3) = 0

Combine like terms: ix2 + -1ix2 = 0
(-48 + 0 + 3i2 + -1i2x + 12x + 28x + -7x2 + -4x2 + x3) = 0
(-48 + 3i2 + -1i2x + 12x + 28x + -7x2 + -4x2 + x3) = 0

Combine like terms: 12x + 28x = 40x
(-48 + 3i2 + -1i2x + 40x + -7x2 + -4x2 + x3) = 0

Combine like terms: -7x2 + -4x2 = -11x2
(-48 + 3i2 + -1i2x + 40x + -11x2 + x3) = 0

Solving
-48 + 3i2 + -1i2x + 40x + -11x2 + x3 = 0

Solving for variable 'i'.

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

Add '48' to each side of the equation.
-48 + 3i2 + -1i2x + 40x + -11x2 + 48 + x3 = 0 + 48

Reorder the terms:
-48 + 48 + 3i2 + -1i2x + 40x + -11x2 + x3 = 0 + 48

Combine like terms: -48 + 48 = 0
0 + 3i2 + -1i2x + 40x + -11x2 + x3 = 0 + 48
3i2 + -1i2x + 40x + -11x2 + x3 = 0 + 48

Combine like terms: 0 + 48 = 48
3i2 + -1i2x + 40x + -11x2 + x3 = 48

Add '-40x' to each side of the equation.
3i2 + -1i2x + 40x + -11x2 + -40x + x3 = 48 + -40x

Reorder the terms:
3i2 + -1i2x + 40x + -40x + -11x2 + x3 = 48 + -40x

Combine like terms: 40x + -40x = 0
3i2 + -1i2x + 0 + -11x2 + x3 = 48 + -40x
3i2 + -1i2x + -11x2 + x3 = 48 + -40x

Add '11x2' to each side of the equation.
3i2 + -1i2x + -11x2 + 11x2 + x3 = 48 + -40x + 11x2

Combine like terms: -11x2 + 11x2 = 0
3i2 + -1i2x + 0 + x3 = 48 + -40x + 11x2
3i2 + -1i2x + x3 = 48 + -40x + 11x2

Add '-1x3' to each side of the equation.
3i2 + -1i2x + x3 + -1x3 = 48 + -40x + 11x2 + -1x3

Combine like terms: x3 + -1x3 = 0
3i2 + -1i2x + 0 = 48 + -40x + 11x2 + -1x3
3i2 + -1i2x = 48 + -40x + 11x2 + -1x3

Reorder the terms:
-48 + 3i2 + -1i2x + 40x + -11x2 + x3 = 48 + -40x + 11x2 + -1x3 + -48 + 40x + -11x2 + x3

Reorder the terms:
-48 + 3i2 + -1i2x + 40x + -11x2 + x3 = 48 + -48 + -40x + 40x + 11x2 + -11x2 + -1x3 + x3

Combine like terms: 48 + -48 = 0
-48 + 3i2 + -1i2x + 40x + -11x2 + x3 = 0 + -40x + 40x + 11x2 + -11x2 + -1x3 + x3
-48 + 3i2 + -1i2x + 40x + -11x2 + x3 = -40x + 40x + 11x2 + -11x2 + -1x3 + x3

Combine like terms: -40x + 40x = 0
-48 + 3i2 + -1i2x + 40x + -11x2 + x3 = 0 + 11x2 + -11x2 + -1x3 + x3
-48 + 3i2 + -1i2x + 40x + -11x2 + x3 = 11x2 + -11x2 + -1x3 + x3

Combine like terms: 11x2 + -11x2 = 0
-48 + 3i2 + -1i2x + 40x + -11x2 + x3 = 0 + -1x3 + x3
-48 + 3i2 + -1i2x + 40x + -11x2 + x3 = -1x3 + x3

Combine like terms: -1x3 + x3 = 0
-48 + 3i2 + -1i2x + 40x + -11x2 + x3 = 0

The solution to this equation could not be determined.

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