(x+4)(x-6-2i)(x-6+2i)=f(x)

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Solution for (x+4)(x-6-2i)(x-6+2i)=f(x) equation: 


Simplifying
(x + 4)(x + -6 + -2i)(x + -6 + 2i) = f(x)

Reorder the terms:
(4 + x)(x + -6 + -2i)(x + -6 + 2i) = f(x)

Reorder the terms:
(4 + x)(-6 + -2i + x)(x + -6 + 2i) = f(x)

Reorder the terms:
(4 + x)(-6 + -2i + x)(-6 + 2i + x) = f(x)

Multiply (4 + x) * (-6 + -2i + x)
(4(-6 + -2i + x) + x(-6 + -2i + x))(-6 + 2i + x) = f(x)
((-6 * 4 + -2i * 4 + x * 4) + x(-6 + -2i + x))(-6 + 2i + x) = f(x)
((-24 + -8i + 4x) + x(-6 + -2i + x))(-6 + 2i + x) = f(x)
(-24 + -8i + 4x + (-6 * x + -2i * x + x * x))(-6 + 2i + x) = f(x)

Reorder the terms:
(-24 + -8i + 4x + (-2ix + -6x + x2))(-6 + 2i + x) = f(x)
(-24 + -8i + 4x + (-2ix + -6x + x2))(-6 + 2i + x) = f(x)

Reorder the terms:
(-24 + -8i + -2ix + 4x + -6x + x2)(-6 + 2i + x) = f(x)

Combine like terms: 4x + -6x = -2x
(-24 + -8i + -2ix + -2x + x2)(-6 + 2i + x) = f(x)

Multiply (-24 + -8i + -2ix + -2x + x2) * (-6 + 2i + x)
(-24(-6 + 2i + x) + -8i * (-6 + 2i + x) + -2ix * (-6 + 2i + x) + -2x * (-6 + 2i + x) + x2(-6 + 2i + x)) = f(x)
((-6 * -24 + 2i * -24 + x * -24) + -8i * (-6 + 2i + x) + -2ix * (-6 + 2i + x) + -2x * (-6 + 2i + x) + x2(-6 + 2i + x)) = f(x)
((144 + -48i + -24x) + -8i * (-6 + 2i + x) + -2ix * (-6 + 2i + x) + -2x * (-6 + 2i + x) + x2(-6 + 2i + x)) = f(x)
(144 + -48i + -24x + (-6 * -8i + 2i * -8i + x * -8i) + -2ix * (-6 + 2i + x) + -2x * (-6 + 2i + x) + x2(-6 + 2i + x)) = f(x)

Reorder the terms:
(144 + -48i + -24x + (48i + -8ix + -16i2) + -2ix * (-6 + 2i + x) + -2x * (-6 + 2i + x) + x2(-6 + 2i + x)) = f(x)
(144 + -48i + -24x + (48i + -8ix + -16i2) + -2ix * (-6 + 2i + x) + -2x * (-6 + 2i + x) + x2(-6 + 2i + x)) = f(x)
(144 + -48i + -24x + 48i + -8ix + -16i2 + (-6 * -2ix + 2i * -2ix + x * -2ix) + -2x * (-6 + 2i + x) + x2(-6 + 2i + x)) = f(x)

Reorder the terms:
(144 + -48i + -24x + 48i + -8ix + -16i2 + (12ix + -2ix2 + -4i2x) + -2x * (-6 + 2i + x) + x2(-6 + 2i + x)) = f(x)
(144 + -48i + -24x + 48i + -8ix + -16i2 + (12ix + -2ix2 + -4i2x) + -2x * (-6 + 2i + x) + x2(-6 + 2i + x)) = f(x)
(144 + -48i + -24x + 48i + -8ix + -16i2 + 12ix + -2ix2 + -4i2x + (-6 * -2x + 2i * -2x + x * -2x) + x2(-6 + 2i + x)) = f(x)

Reorder the terms:
(144 + -48i + -24x + 48i + -8ix + -16i2 + 12ix + -2ix2 + -4i2x + (-4ix + 12x + -2x2) + x2(-6 + 2i + x)) = f(x)
(144 + -48i + -24x + 48i + -8ix + -16i2 + 12ix + -2ix2 + -4i2x + (-4ix + 12x + -2x2) + x2(-6 + 2i + x)) = f(x)
(144 + -48i + -24x + 48i + -8ix + -16i2 + 12ix + -2ix2 + -4i2x + -4ix + 12x + -2x2 + (-6 * x2 + 2i * x2 + x * x2)) = f(x)

Reorder the terms:
(144 + -48i + -24x + 48i + -8ix + -16i2 + 12ix + -2ix2 + -4i2x + -4ix + 12x + -2x2 + (2ix2 + -6x2 + x3)) = f(x)
(144 + -48i + -24x + 48i + -8ix + -16i2 + 12ix + -2ix2 + -4i2x + -4ix + 12x + -2x2 + (2ix2 + -6x2 + x3)) = f(x)

Reorder the terms:
(144 + -48i + 48i + -8ix + 12ix + -4ix + -2ix2 + 2ix2 + -16i2 + -4i2x + -24x + 12x + -2x2 + -6x2 + x3) = f(x)

Combine like terms: -48i + 48i = 0
(144 + 0 + -8ix + 12ix + -4ix + -2ix2 + 2ix2 + -16i2 + -4i2x + -24x + 12x + -2x2 + -6x2 + x3) = f(x)
(144 + -8ix + 12ix + -4ix + -2ix2 + 2ix2 + -16i2 + -4i2x + -24x + 12x + -2x2 + -6x2 + x3) = f(x)

Combine like terms: -8ix + 12ix = 4ix
(144 + 4ix + -4ix + -2ix2 + 2ix2 + -16i2 + -4i2x + -24x + 12x + -2x2 + -6x2 + x3) = f(x)

Combine like terms: 4ix + -4ix = 0
(144 + 0 + -2ix2 + 2ix2 + -16i2 + -4i2x + -24x + 12x + -2x2 + -6x2 + x3) = f(x)
(144 + -2ix2 + 2ix2 + -16i2 + -4i2x + -24x + 12x + -2x2 + -6x2 + x3) = f(x)

Combine like terms: -2ix2 + 2ix2 = 0
(144 + 0 + -16i2 + -4i2x + -24x + 12x + -2x2 + -6x2 + x3) = f(x)
(144 + -16i2 + -4i2x + -24x + 12x + -2x2 + -6x2 + x3) = f(x)

Combine like terms: -24x + 12x = -12x
(144 + -16i2 + -4i2x + -12x + -2x2 + -6x2 + x3) = f(x)

Combine like terms: -2x2 + -6x2 = -8x2
(144 + -16i2 + -4i2x + -12x + -8x2 + x3) = f(x)

Multiply f * x
144 + -16i2 + -4i2x + -12x + -8x2 + x3 = fx

Solving
144 + -16i2 + -4i2x + -12x + -8x2 + x3 = fx

Solving for variable 'i'.

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

Add '-144' to each side of the equation.
144 + -16i2 + -4i2x + -12x + -8x2 + -144 + x3 = -144 + fx

Reorder the terms:
144 + -144 + -16i2 + -4i2x + -12x + -8x2 + x3 = -144 + fx

Combine like terms: 144 + -144 = 0
0 + -16i2 + -4i2x + -12x + -8x2 + x3 = -144 + fx
-16i2 + -4i2x + -12x + -8x2 + x3 = -144 + fx

Add '12x' to each side of the equation.
-16i2 + -4i2x + -12x + -8x2 + 12x + x3 = -144 + fx + 12x

Reorder the terms:
-16i2 + -4i2x + -12x + 12x + -8x2 + x3 = -144 + fx + 12x

Combine like terms: -12x + 12x = 0
-16i2 + -4i2x + 0 + -8x2 + x3 = -144 + fx + 12x
-16i2 + -4i2x + -8x2 + x3 = -144 + fx + 12x

Add '8x2' to each side of the equation.
-16i2 + -4i2x + -8x2 + 8x2 + x3 = -144 + fx + 12x + 8x2

Combine like terms: -8x2 + 8x2 = 0
-16i2 + -4i2x + 0 + x3 = -144 + fx + 12x + 8x2
-16i2 + -4i2x + x3 = -144 + fx + 12x + 8x2

Add '-1x3' to each side of the equation.
-16i2 + -4i2x + x3 + -1x3 = -144 + fx + 12x + 8x2 + -1x3

Combine like terms: x3 + -1x3 = 0
-16i2 + -4i2x + 0 = -144 + fx + 12x + 8x2 + -1x3
-16i2 + -4i2x = -144 + fx + 12x + 8x2 + -1x3

Reorder the terms:
144 + -1fx + -16i2 + -4i2x + -12x + -8x2 + x3 = -144 + fx + 12x + 8x2 + -1x3 + 144 + -1fx + -12x + -8x2 + x3

Reorder the terms:
144 + -1fx + -16i2 + -4i2x + -12x + -8x2 + x3 = -144 + 144 + fx + -1fx + 12x + -12x + 8x2 + -8x2 + -1x3 + x3

Combine like terms: -144 + 144 = 0
144 + -1fx + -16i2 + -4i2x + -12x + -8x2 + x3 = 0 + fx + -1fx + 12x + -12x + 8x2 + -8x2 + -1x3 + x3
144 + -1fx + -16i2 + -4i2x + -12x + -8x2 + x3 = fx + -1fx + 12x + -12x + 8x2 + -8x2 + -1x3 + x3

Combine like terms: fx + -1fx = 0
144 + -1fx + -16i2 + -4i2x + -12x + -8x2 + x3 = 0 + 12x + -12x + 8x2 + -8x2 + -1x3 + x3
144 + -1fx + -16i2 + -4i2x + -12x + -8x2 + x3 = 12x + -12x + 8x2 + -8x2 + -1x3 + x3

Combine like terms: 12x + -12x = 0
144 + -1fx + -16i2 + -4i2x + -12x + -8x2 + x3 = 0 + 8x2 + -8x2 + -1x3 + x3
144 + -1fx + -16i2 + -4i2x + -12x + -8x2 + x3 = 8x2 + -8x2 + -1x3 + x3

Combine like terms: 8x2 + -8x2 = 0
144 + -1fx + -16i2 + -4i2x + -12x + -8x2 + x3 = 0 + -1x3 + x3
144 + -1fx + -16i2 + -4i2x + -12x + -8x2 + x3 = -1x3 + x3

Combine like terms: -1x3 + x3 = 0
144 + -1fx + -16i2 + -4i2x + -12x + -8x2 + x3 = 0

The solution to this equation could not be determined.

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