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

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


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

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

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

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

Multiply (-4 + -1i + x) * (-4 + 1i + x)
0 = (-4(-4 + 1i + x) + -1i * (-4 + 1i + x) + x(-4 + 1i + x))(-4 + x)
0 = ((-4 * -4 + 1i * -4 + x * -4) + -1i * (-4 + 1i + x) + x(-4 + 1i + x))(-4 + x)
0 = ((16 + -4i + -4x) + -1i * (-4 + 1i + x) + x(-4 + 1i + x))(-4 + x)
0 = (16 + -4i + -4x + (-4 * -1i + 1i * -1i + x * -1i) + x(-4 + 1i + x))(-4 + x)

Reorder the terms:
0 = (16 + -4i + -4x + (4i + -1ix + -1i2) + x(-4 + 1i + x))(-4 + x)
0 = (16 + -4i + -4x + (4i + -1ix + -1i2) + x(-4 + 1i + x))(-4 + x)
0 = (16 + -4i + -4x + 4i + -1ix + -1i2 + (-4 * x + 1i * x + x * x))(-4 + x)

Reorder the terms:
0 = (16 + -4i + -4x + 4i + -1ix + -1i2 + (1ix + -4x + x2))(-4 + x)
0 = (16 + -4i + -4x + 4i + -1ix + -1i2 + (1ix + -4x + x2))(-4 + x)

Reorder the terms:
0 = (16 + -4i + 4i + -1ix + 1ix + -1i2 + -4x + -4x + x2)(-4 + x)

Combine like terms: -4i + 4i = 0
0 = (16 + 0 + -1ix + 1ix + -1i2 + -4x + -4x + x2)(-4 + x)
0 = (16 + -1ix + 1ix + -1i2 + -4x + -4x + x2)(-4 + x)

Combine like terms: -1ix + 1ix = 0
0 = (16 + 0 + -1i2 + -4x + -4x + x2)(-4 + x)
0 = (16 + -1i2 + -4x + -4x + x2)(-4 + x)

Combine like terms: -4x + -4x = -8x
0 = (16 + -1i2 + -8x + x2)(-4 + x)

Multiply (16 + -1i2 + -8x + x2) * (-4 + x)
0 = (16(-4 + x) + -1i2 * (-4 + x) + -8x * (-4 + x) + x2(-4 + x))
0 = ((-4 * 16 + x * 16) + -1i2 * (-4 + x) + -8x * (-4 + x) + x2(-4 + x))
0 = ((-64 + 16x) + -1i2 * (-4 + x) + -8x * (-4 + x) + x2(-4 + x))
0 = (-64 + 16x + (-4 * -1i2 + x * -1i2) + -8x * (-4 + x) + x2(-4 + x))
0 = (-64 + 16x + (4i2 + -1i2x) + -8x * (-4 + x) + x2(-4 + x))
0 = (-64 + 16x + 4i2 + -1i2x + (-4 * -8x + x * -8x) + x2(-4 + x))
0 = (-64 + 16x + 4i2 + -1i2x + (32x + -8x2) + x2(-4 + x))
0 = (-64 + 16x + 4i2 + -1i2x + 32x + -8x2 + (-4 * x2 + x * x2))
0 = (-64 + 16x + 4i2 + -1i2x + 32x + -8x2 + (-4x2 + x3))

Reorder the terms:
0 = (-64 + 4i2 + -1i2x + 16x + 32x + -8x2 + -4x2 + x3)

Combine like terms: 16x + 32x = 48x
0 = (-64 + 4i2 + -1i2x + 48x + -8x2 + -4x2 + x3)

Combine like terms: -8x2 + -4x2 = -12x2
0 = (-64 + 4i2 + -1i2x + 48x + -12x2 + x3)

Solving
0 = -64 + 4i2 + -1i2x + 48x + -12x2 + x3

Solving for variable 'i'.

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

Add '-4i2' to each side of the equation.
0 + -4i2 = -64 + 4i2 + -1i2x + 48x + -12x2 + -4i2 + x3
Remove the zero:
-4i2 = -64 + 4i2 + -1i2x + 48x + -12x2 + -4i2 + x3

Reorder the terms:
-4i2 = -64 + 4i2 + -4i2 + -1i2x + 48x + -12x2 + x3

Combine like terms: 4i2 + -4i2 = 0
-4i2 = -64 + 0 + -1i2x + 48x + -12x2 + x3
-4i2 = -64 + -1i2x + 48x + -12x2 + x3

Add 'i2x' to each side of the equation.
-4i2 + i2x = -64 + -1i2x + 48x + -12x2 + i2x + x3

Reorder the terms:
-4i2 + i2x = -64 + -1i2x + i2x + 48x + -12x2 + x3

Combine like terms: -1i2x + i2x = 0
-4i2 + i2x = -64 + 0 + 48x + -12x2 + x3
-4i2 + i2x = -64 + 48x + -12x2 + x3

Reorder the terms:
64 + -4i2 + i2x + -48x + 12x2 + -1x3 = -64 + 48x + -12x2 + x3 + 64 + -48x + 12x2 + -1x3

Reorder the terms:
64 + -4i2 + i2x + -48x + 12x2 + -1x3 = -64 + 64 + 48x + -48x + -12x2 + 12x2 + x3 + -1x3

Combine like terms: -64 + 64 = 0
64 + -4i2 + i2x + -48x + 12x2 + -1x3 = 0 + 48x + -48x + -12x2 + 12x2 + x3 + -1x3
64 + -4i2 + i2x + -48x + 12x2 + -1x3 = 48x + -48x + -12x2 + 12x2 + x3 + -1x3

Combine like terms: 48x + -48x = 0
64 + -4i2 + i2x + -48x + 12x2 + -1x3 = 0 + -12x2 + 12x2 + x3 + -1x3
64 + -4i2 + i2x + -48x + 12x2 + -1x3 = -12x2 + 12x2 + x3 + -1x3

Combine like terms: -12x2 + 12x2 = 0
64 + -4i2 + i2x + -48x + 12x2 + -1x3 = 0 + x3 + -1x3
64 + -4i2 + i2x + -48x + 12x2 + -1x3 = x3 + -1x3

Combine like terms: x3 + -1x3 = 0
64 + -4i2 + i2x + -48x + 12x2 + -1x3 = 0

The solution to this equation could not be determined.

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