(x-(4-4i))(x-(4+4i))(x-5)(x-5)=f(x)

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Solution for (x-(4-4i))(x-(4+4i))(x-5)(x-5)=f(x) equation:


Simplifying
(x + -1(4 + -4i))(x + -1(4 + 4i))(x + -5)(x + -5) = f(x)
(x + (4 * -1 + -4i * -1))(x + -1(4 + 4i))(x + -5)(x + -5) = f(x)
(x + (-4 + 4i))(x + -1(4 + 4i))(x + -5)(x + -5) = f(x)

Reorder the terms:
(-4 + 4i + x)(x + -1(4 + 4i))(x + -5)(x + -5) = f(x)
(-4 + 4i + x)(x + (4 * -1 + 4i * -1))(x + -5)(x + -5) = f(x)
(-4 + 4i + x)(x + (-4 + -4i))(x + -5)(x + -5) = f(x)

Reorder the terms:
(-4 + 4i + x)(-4 + -4i + x)(x + -5)(x + -5) = f(x)

Reorder the terms:
(-4 + 4i + x)(-4 + -4i + x)(-5 + x)(x + -5) = f(x)

Reorder the terms:
(-4 + 4i + x)(-4 + -4i + x)(-5 + x)(-5 + x) = f(x)

Multiply (-4 + 4i + x) * (-4 + -4i + x)
(-4(-4 + -4i + x) + 4i * (-4 + -4i + x) + x(-4 + -4i + x))(-5 + x)(-5 + x) = f(x)
((-4 * -4 + -4i * -4 + x * -4) + 4i * (-4 + -4i + x) + x(-4 + -4i + x))(-5 + x)(-5 + x) = f(x)
((16 + 16i + -4x) + 4i * (-4 + -4i + x) + x(-4 + -4i + x))(-5 + x)(-5 + x) = f(x)
(16 + 16i + -4x + (-4 * 4i + -4i * 4i + x * 4i) + x(-4 + -4i + x))(-5 + x)(-5 + x) = f(x)

Reorder the terms:
(16 + 16i + -4x + (-16i + 4ix + -16i2) + x(-4 + -4i + x))(-5 + x)(-5 + x) = f(x)
(16 + 16i + -4x + (-16i + 4ix + -16i2) + x(-4 + -4i + x))(-5 + x)(-5 + x) = f(x)
(16 + 16i + -4x + -16i + 4ix + -16i2 + (-4 * x + -4i * x + x * x))(-5 + x)(-5 + x) = f(x)

Reorder the terms:
(16 + 16i + -4x + -16i + 4ix + -16i2 + (-4ix + -4x + x2))(-5 + x)(-5 + x) = f(x)
(16 + 16i + -4x + -16i + 4ix + -16i2 + (-4ix + -4x + x2))(-5 + x)(-5 + x) = f(x)

Reorder the terms:
(16 + 16i + -16i + 4ix + -4ix + -16i2 + -4x + -4x + x2)(-5 + x)(-5 + x) = f(x)

Combine like terms: 16i + -16i = 0
(16 + 0 + 4ix + -4ix + -16i2 + -4x + -4x + x2)(-5 + x)(-5 + x) = f(x)
(16 + 4ix + -4ix + -16i2 + -4x + -4x + x2)(-5 + x)(-5 + x) = f(x)

Combine like terms: 4ix + -4ix = 0
(16 + 0 + -16i2 + -4x + -4x + x2)(-5 + x)(-5 + x) = f(x)
(16 + -16i2 + -4x + -4x + x2)(-5 + x)(-5 + x) = f(x)

Combine like terms: -4x + -4x = -8x
(16 + -16i2 + -8x + x2)(-5 + x)(-5 + x) = f(x)

Multiply (16 + -16i2 + -8x + x2) * (-5 + x)
(16(-5 + x) + -16i2 * (-5 + x) + -8x * (-5 + x) + x2(-5 + x))(-5 + x) = f(x)
((-5 * 16 + x * 16) + -16i2 * (-5 + x) + -8x * (-5 + x) + x2(-5 + x))(-5 + x) = f(x)
((-80 + 16x) + -16i2 * (-5 + x) + -8x * (-5 + x) + x2(-5 + x))(-5 + x) = f(x)
(-80 + 16x + (-5 * -16i2 + x * -16i2) + -8x * (-5 + x) + x2(-5 + x))(-5 + x) = f(x)
(-80 + 16x + (80i2 + -16i2x) + -8x * (-5 + x) + x2(-5 + x))(-5 + x) = f(x)
(-80 + 16x + 80i2 + -16i2x + (-5 * -8x + x * -8x) + x2(-5 + x))(-5 + x) = f(x)
(-80 + 16x + 80i2 + -16i2x + (40x + -8x2) + x2(-5 + x))(-5 + x) = f(x)
(-80 + 16x + 80i2 + -16i2x + 40x + -8x2 + (-5 * x2 + x * x2))(-5 + x) = f(x)
(-80 + 16x + 80i2 + -16i2x + 40x + -8x2 + (-5x2 + x3))(-5 + x) = f(x)

Reorder the terms:
(-80 + 80i2 + -16i2x + 16x + 40x + -8x2 + -5x2 + x3)(-5 + x) = f(x)

Combine like terms: 16x + 40x = 56x
(-80 + 80i2 + -16i2x + 56x + -8x2 + -5x2 + x3)(-5 + x) = f(x)

Combine like terms: -8x2 + -5x2 = -13x2
(-80 + 80i2 + -16i2x + 56x + -13x2 + x3)(-5 + x) = f(x)

Multiply (-80 + 80i2 + -16i2x + 56x + -13x2 + x3) * (-5 + x)
(-80(-5 + x) + 80i2 * (-5 + x) + -16i2x * (-5 + x) + 56x * (-5 + x) + -13x2 * (-5 + x) + x3(-5 + x)) = f(x)
((-5 * -80 + x * -80) + 80i2 * (-5 + x) + -16i2x * (-5 + x) + 56x * (-5 + x) + -13x2 * (-5 + x) + x3(-5 + x)) = f(x)
((400 + -80x) + 80i2 * (-5 + x) + -16i2x * (-5 + x) + 56x * (-5 + x) + -13x2 * (-5 + x) + x3(-5 + x)) = f(x)
(400 + -80x + (-5 * 80i2 + x * 80i2) + -16i2x * (-5 + x) + 56x * (-5 + x) + -13x2 * (-5 + x) + x3(-5 + x)) = f(x)
(400 + -80x + (-400i2 + 80i2x) + -16i2x * (-5 + x) + 56x * (-5 + x) + -13x2 * (-5 + x) + x3(-5 + x)) = f(x)
(400 + -80x + -400i2 + 80i2x + (-5 * -16i2x + x * -16i2x) + 56x * (-5 + x) + -13x2 * (-5 + x) + x3(-5 + x)) = f(x)
(400 + -80x + -400i2 + 80i2x + (80i2x + -16i2x2) + 56x * (-5 + x) + -13x2 * (-5 + x) + x3(-5 + x)) = f(x)
(400 + -80x + -400i2 + 80i2x + 80i2x + -16i2x2 + (-5 * 56x + x * 56x) + -13x2 * (-5 + x) + x3(-5 + x)) = f(x)
(400 + -80x + -400i2 + 80i2x + 80i2x + -16i2x2 + (-280x + 56x2) + -13x2 * (-5 + x) + x3(-5 + x)) = f(x)
(400 + -80x + -400i2 + 80i2x + 80i2x + -16i2x2 + -280x + 56x2 + (-5 * -13x2 + x * -13x2) + x3(-5 + x)) = f(x)
(400 + -80x + -400i2 + 80i2x + 80i2x + -16i2x2 + -280x + 56x2 + (65x2 + -13x3) + x3(-5 + x)) = f(x)
(400 + -80x + -400i2 + 80i2x + 80i2x + -16i2x2 + -280x + 56x2 + 65x2 + -13x3 + (-5 * x3 + x * x3)) = f(x)
(400 + -80x + -400i2 + 80i2x + 80i2x + -16i2x2 + -280x + 56x2 + 65x2 + -13x3 + (-5x3 + x4)) = f(x)

Reorder the terms:
(400 + -400i2 + 80i2x + 80i2x + -16i2x2 + -80x + -280x + 56x2 + 65x2 + -13x3 + -5x3 + x4) = f(x)

Combine like terms: 80i2x + 80i2x = 160i2x
(400 + -400i2 + 160i2x + -16i2x2 + -80x + -280x + 56x2 + 65x2 + -13x3 + -5x3 + x4) = f(x)

Combine like terms: -80x + -280x = -360x
(400 + -400i2 + 160i2x + -16i2x2 + -360x + 56x2 + 65x2 + -13x3 + -5x3 + x4) = f(x)

Combine like terms: 56x2 + 65x2 = 121x2
(400 + -400i2 + 160i2x + -16i2x2 + -360x + 121x2 + -13x3 + -5x3 + x4) = f(x)

Combine like terms: -13x3 + -5x3 = -18x3
(400 + -400i2 + 160i2x + -16i2x2 + -360x + 121x2 + -18x3 + x4) = f(x)

Multiply f * x
400 + -400i2 + 160i2x + -16i2x2 + -360x + 121x2 + -18x3 + x4 = fx

Solving
400 + -400i2 + 160i2x + -16i2x2 + -360x + 121x2 + -18x3 + x4 = fx

Solving for variable 'i'.

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

Add '-400' to each side of the equation.
400 + -400i2 + 160i2x + -16i2x2 + -360x + 121x2 + -18x3 + -400 + x4 = -400 + fx

Reorder the terms:
400 + -400 + -400i2 + 160i2x + -16i2x2 + -360x + 121x2 + -18x3 + x4 = -400 + fx

Combine like terms: 400 + -400 = 0
0 + -400i2 + 160i2x + -16i2x2 + -360x + 121x2 + -18x3 + x4 = -400 + fx
-400i2 + 160i2x + -16i2x2 + -360x + 121x2 + -18x3 + x4 = -400 + fx

Add '360x' to each side of the equation.
-400i2 + 160i2x + -16i2x2 + -360x + 121x2 + -18x3 + 360x + x4 = -400 + fx + 360x

Reorder the terms:
-400i2 + 160i2x + -16i2x2 + -360x + 360x + 121x2 + -18x3 + x4 = -400 + fx + 360x

Combine like terms: -360x + 360x = 0
-400i2 + 160i2x + -16i2x2 + 0 + 121x2 + -18x3 + x4 = -400 + fx + 360x
-400i2 + 160i2x + -16i2x2 + 121x2 + -18x3 + x4 = -400 + fx + 360x

Add '-121x2' to each side of the equation.
-400i2 + 160i2x + -16i2x2 + 121x2 + -18x3 + -121x2 + x4 = -400 + fx + 360x + -121x2

Reorder the terms:
-400i2 + 160i2x + -16i2x2 + 121x2 + -121x2 + -18x3 + x4 = -400 + fx + 360x + -121x2

Combine like terms: 121x2 + -121x2 = 0
-400i2 + 160i2x + -16i2x2 + 0 + -18x3 + x4 = -400 + fx + 360x + -121x2
-400i2 + 160i2x + -16i2x2 + -18x3 + x4 = -400 + fx + 360x + -121x2

Add '18x3' to each side of the equation.
-400i2 + 160i2x + -16i2x2 + -18x3 + 18x3 + x4 = -400 + fx + 360x + -121x2 + 18x3

Combine like terms: -18x3 + 18x3 = 0
-400i2 + 160i2x + -16i2x2 + 0 + x4 = -400 + fx + 360x + -121x2 + 18x3
-400i2 + 160i2x + -16i2x2 + x4 = -400 + fx + 360x + -121x2 + 18x3

Add '-1x4' to each side of the equation.
-400i2 + 160i2x + -16i2x2 + x4 + -1x4 = -400 + fx + 360x + -121x2 + 18x3 + -1x4

Combine like terms: x4 + -1x4 = 0
-400i2 + 160i2x + -16i2x2 + 0 = -400 + fx + 360x + -121x2 + 18x3 + -1x4
-400i2 + 160i2x + -16i2x2 = -400 + fx + 360x + -121x2 + 18x3 + -1x4

Reorder the terms:
400 + -1fx + -400i2 + 160i2x + -16i2x2 + -360x + 121x2 + -18x3 + x4 = -400 + fx + 360x + -121x2 + 18x3 + -1x4 + 400 + -1fx + -360x + 121x2 + -18x3 + x4

Reorder the terms:
400 + -1fx + -400i2 + 160i2x + -16i2x2 + -360x + 121x2 + -18x3 + x4 = -400 + 400 + fx + -1fx + 360x + -360x + -121x2 + 121x2 + 18x3 + -18x3 + -1x4 + x4

Combine like terms: -400 + 400 = 0
400 + -1fx + -400i2 + 160i2x + -16i2x2 + -360x + 121x2 + -18x3 + x4 = 0 + fx + -1fx + 360x + -360x + -121x2 + 121x2 + 18x3 + -18x3 + -1x4 + x4
400 + -1fx + -400i2 + 160i2x + -16i2x2 + -360x + 121x2 + -18x3 + x4 = fx + -1fx + 360x + -360x + -121x2 + 121x2 + 18x3 + -18x3 + -1x4 + x4

Combine like terms: fx + -1fx = 0
400 + -1fx + -400i2 + 160i2x + -16i2x2 + -360x + 121x2 + -18x3 + x4 = 0 + 360x + -360x + -121x2 + 121x2 + 18x3 + -18x3 + -1x4 + x4
400 + -1fx + -400i2 + 160i2x + -16i2x2 + -360x + 121x2 + -18x3 + x4 = 360x + -360x + -121x2 + 121x2 + 18x3 + -18x3 + -1x4 + x4

Combine like terms: 360x + -360x = 0
400 + -1fx + -400i2 + 160i2x + -16i2x2 + -360x + 121x2 + -18x3 + x4 = 0 + -121x2 + 121x2 + 18x3 + -18x3 + -1x4 + x4
400 + -1fx + -400i2 + 160i2x + -16i2x2 + -360x + 121x2 + -18x3 + x4 = -121x2 + 121x2 + 18x3 + -18x3 + -1x4 + x4

Combine like terms: -121x2 + 121x2 = 0
400 + -1fx + -400i2 + 160i2x + -16i2x2 + -360x + 121x2 + -18x3 + x4 = 0 + 18x3 + -18x3 + -1x4 + x4
400 + -1fx + -400i2 + 160i2x + -16i2x2 + -360x + 121x2 + -18x3 + x4 = 18x3 + -18x3 + -1x4 + x4

Combine like terms: 18x3 + -18x3 = 0
400 + -1fx + -400i2 + 160i2x + -16i2x2 + -360x + 121x2 + -18x3 + x4 = 0 + -1x4 + x4
400 + -1fx + -400i2 + 160i2x + -16i2x2 + -360x + 121x2 + -18x3 + x4 = -1x4 + x4

Combine like terms: -1x4 + x4 = 0
400 + -1fx + -400i2 + 160i2x + -16i2x2 + -360x + 121x2 + -18x3 + x4 = 0

The solution to this equation could not be determined.

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