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

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


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

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

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

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

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

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

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

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

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

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

Solving
0 = 16 + -1i2 + -8x + x2

Solving for variable 'i'.

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

Add 'i2' to each side of the equation.
0 + i2 = 16 + -1i2 + -8x + i2 + x2
Remove the zero:
i2 = 16 + -1i2 + -8x + i2 + x2

Reorder the terms:
i2 = 16 + -1i2 + i2 + -8x + x2

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

Simplifying
i2 = 16 + -8x + x2

Reorder the terms:
-16 + i2 + 8x + -1x2 = 16 + -8x + x2 + -16 + 8x + -1x2

Reorder the terms:
-16 + i2 + 8x + -1x2 = 16 + -16 + -8x + 8x + x2 + -1x2

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

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

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

The solution to this equation could not be determined.

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