f(x)=(x+4i)(x-4i)(x-4)(x-(1-i))(x-(1+i))

Simple and best practice solution for f(x)=(x+4i)(x-4i)(x-4)(x-(1-i))(x-(1+i)) equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

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Solution for f(x)=(x+4i)(x-4i)(x-4)(x-(1-i))(x-(1+i)) equation: 


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

Multiply f * x
fx = (x + 4i)(x + -4i)(x + -4)(x + -1(1 + -1i))(x + -1(1 + i))

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

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

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

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

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

Multiply (4i + x) * (-4i + x)
fx = (4i * (-4i + x) + x(-4i + x))(-4 + x)(-1 + 1i + x)(-1 + -1i + x)
fx = ((-4i * 4i + x * 4i) + x(-4i + x))(-4 + x)(-1 + 1i + x)(-1 + -1i + x)

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

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

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

Multiply (-16i2 + x2) * (-4 + x)
fx = (-16i2 * (-4 + x) + x2(-4 + x))(-1 + 1i + x)(-1 + -1i + x)
fx = ((-4 * -16i2 + x * -16i2) + x2(-4 + x))(-1 + 1i + x)(-1 + -1i + x)
fx = ((64i2 + -16i2x) + x2(-4 + x))(-1 + 1i + x)(-1 + -1i + x)
fx = (64i2 + -16i2x + (-4 * x2 + x * x2))(-1 + 1i + x)(-1 + -1i + x)
fx = (64i2 + -16i2x + (-4x2 + x3))(-1 + 1i + x)(-1 + -1i + x)
fx = (64i2 + -16i2x + -4x2 + x3)(-1 + 1i + x)(-1 + -1i + x)

Multiply (64i2 + -16i2x + -4x2 + x3) * (-1 + 1i + x)
fx = (64i2 * (-1 + 1i + x) + -16i2x * (-1 + 1i + x) + -4x2 * (-1 + 1i + x) + x3(-1 + 1i + x))(-1 + -1i + x)
fx = ((-1 * 64i2 + 1i * 64i2 + x * 64i2) + -16i2x * (-1 + 1i + x) + -4x2 * (-1 + 1i + x) + x3(-1 + 1i + x))(-1 + -1i + x)

Reorder the terms:
fx = ((-64i2 + 64i2x + 64i3) + -16i2x * (-1 + 1i + x) + -4x2 * (-1 + 1i + x) + x3(-1 + 1i + x))(-1 + -1i + x)
fx = ((-64i2 + 64i2x + 64i3) + -16i2x * (-1 + 1i + x) + -4x2 * (-1 + 1i + x) + x3(-1 + 1i + x))(-1 + -1i + x)
fx = (-64i2 + 64i2x + 64i3 + (-1 * -16i2x + 1i * -16i2x + x * -16i2x) + -4x2 * (-1 + 1i + x) + x3(-1 + 1i + x))(-1 + -1i + x)

Reorder the terms:
fx = (-64i2 + 64i2x + 64i3 + (16i2x + -16i2x2 + -16i3x) + -4x2 * (-1 + 1i + x) + x3(-1 + 1i + x))(-1 + -1i + x)
fx = (-64i2 + 64i2x + 64i3 + (16i2x + -16i2x2 + -16i3x) + -4x2 * (-1 + 1i + x) + x3(-1 + 1i + x))(-1 + -1i + x)
fx = (-64i2 + 64i2x + 64i3 + 16i2x + -16i2x2 + -16i3x + (-1 * -4x2 + 1i * -4x2 + x * -4x2) + x3(-1 + 1i + x))(-1 + -1i + x)

Reorder the terms:
fx = (-64i2 + 64i2x + 64i3 + 16i2x + -16i2x2 + -16i3x + (-4ix2 + 4x2 + -4x3) + x3(-1 + 1i + x))(-1 + -1i + x)
fx = (-64i2 + 64i2x + 64i3 + 16i2x + -16i2x2 + -16i3x + (-4ix2 + 4x2 + -4x3) + x3(-1 + 1i + x))(-1 + -1i + x)
fx = (-64i2 + 64i2x + 64i3 + 16i2x + -16i2x2 + -16i3x + -4ix2 + 4x2 + -4x3 + (-1 * x3 + 1i * x3 + x * x3))(-1 + -1i + x)

Reorder the terms:
fx = (-64i2 + 64i2x + 64i3 + 16i2x + -16i2x2 + -16i3x + -4ix2 + 4x2 + -4x3 + (1ix3 + -1x3 + x4))(-1 + -1i + x)
fx = (-64i2 + 64i2x + 64i3 + 16i2x + -16i2x2 + -16i3x + -4ix2 + 4x2 + -4x3 + (1ix3 + -1x3 + x4))(-1 + -1i + x)

Reorder the terms:
fx = (-4ix2 + 1ix3 + -64i2 + 64i2x + 16i2x + -16i2x2 + 64i3 + -16i3x + 4x2 + -4x3 + -1x3 + x4)(-1 + -1i + x)

Combine like terms: 64i2x + 16i2x = 80i2x
fx = (-4ix2 + 1ix3 + -64i2 + 80i2x + -16i2x2 + 64i3 + -16i3x + 4x2 + -4x3 + -1x3 + x4)(-1 + -1i + x)

Combine like terms: -4x3 + -1x3 = -5x3
fx = (-4ix2 + 1ix3 + -64i2 + 80i2x + -16i2x2 + 64i3 + -16i3x + 4x2 + -5x3 + x4)(-1 + -1i + x)

Multiply (-4ix2 + 1ix3 + -64i2 + 80i2x + -16i2x2 + 64i3 + -16i3x + 4x2 + -5x3 + x4) * (-1 + -1i + x)
fx = (-4ix2 * (-1 + -1i + x) + 1ix3 * (-1 + -1i + x) + -64i2 * (-1 + -1i + x) + 80i2x * (-1 + -1i + x) + -16i2x2 * (-1 + -1i + x) + 64i3 * (-1 + -1i + x) + -16i3x * (-1 + -1i + x) + 4x2 * (-1 + -1i + x) + -5x3 * (-1 + -1i + x) + x4(-1 + -1i + x))
fx = ((-1 * -4ix2 + -1i * -4ix2 + x * -4ix2) + 1ix3 * (-1 + -1i + x) + -64i2 * (-1 + -1i + x) + 80i2x * (-1 + -1i + x) + -16i2x2 * (-1 + -1i + x) + 64i3 * (-1 + -1i + x) + -16i3x * (-1 + -1i + x) + 4x2 * (-1 + -1i + x) + -5x3 * (-1 + -1i + x) + x4(-1 + -1i + x))

Reorder the terms:
fx = ((4ix2 + -4ix3 + 4i2x2) + 1ix3 * (-1 + -1i + x) + -64i2 * (-1 + -1i + x) + 80i2x * (-1 + -1i + x) + -16i2x2 * (-1 + -1i + x) + 64i3 * (-1 + -1i + x) + -16i3x * (-1 + -1i + x) + 4x2 * (-1 + -1i + x) + -5x3 * (-1 + -1i + x) + x4(-1 + -1i + x))
fx = ((4ix2 + -4ix3 + 4i2x2) + 1ix3 * (-1 + -1i + x) + -64i2 * (-1 + -1i + x) + 80i2x * (-1 + -1i + x) + -16i2x2 * (-1 + -1i + x) + 64i3 * (-1 + -1i + x) + -16i3x * (-1 + -1i + x) + 4x2 * (-1 + -1i + x) + -5x3 * (-1 + -1i + x) + x4(-1 + -1i + x))
fx = (4ix2 + -4ix3 + 4i2x2 + (-1 * 1ix3 + -1i * 1ix3 + x * 1ix3) + -64i2 * (-1 + -1i + x) + 80i2x * (-1 + -1i + x) + -16i2x2 * (-1 + -1i + x) + 64i3 * (-1 + -1i + x) + -16i3x * (-1 + -1i + x) + 4x2 * (-1 + -1i + x) + -5x3 * (-1 + -1i + x) + x4(-1 + -1i + x))

Reorder the terms:
fx = (4ix2 + -4ix3 + 4i2x2 + (-1ix3 + 1ix4 + -1i2x3) + -64i2 * (-1 + -1i + x) + 80i2x * (-1 + -1i + x) + -16i2x2 * (-1 + -1i + x) + 64i3 * (-1 + -1i + x) + -16i3x * (-1 + -1i + x) + 4x2 * (-1 + -1i + x) + -5x3 * (-1 + -1i + x) + x4(-1 + -1i + x))
fx = (4ix2 + -4ix3 + 4i2x2 + (-1ix3 + 1ix4 + -1i2x3) + -64i2 * (-1 + -1i + x) + 80i2x * (-1 + -1i + x) + -16i2x2 * (-1 + -1i + x) + 64i3 * (-1 + -1i + x) + -16i3x * (-1 + -1i + x) + 4x2 * (-1 + -1i + x) + -5x3 * (-1 + -1i + x) + x4(-1 + -1i + x))
fx = (4ix2 + -4ix3 + 4i2x2 + -1ix3 + 1ix4 + -1i2x3 + (-1 * -64i2 + -1i * -64i2 + x * -64i2) + 80i2x * (-1 + -1i + x) + -16i2x2 * (-1 + -1i + x) + 64i3 * (-1 + -1i + x) + -16i3x * (-1 + -1i + x) + 4x2 * (-1 + -1i + x) + -5x3 * (-1 + -1i + x) + x4(-1 + -1i + x))

Reorder the terms:
fx = (4ix2 + -4ix3 + 4i2x2 + -1ix3 + 1ix4 + -1i2x3 + (64i2 + -64i2x + 64i3) + 80i2x * (-1 + -1i + x) + -16i2x2 * (-1 + -1i + x) + 64i3 * (-1 + -1i + x) + -16i3x * (-1 + -1i + x) + 4x2 * (-1 + -1i + x) + -5x3 * (-1 + -1i + x) + x4(-1 + -1i + x))
fx = (4ix2 + -4ix3 + 4i2x2 + -1ix3 + 1ix4 + -1i2x3 + (64i2 + -64i2x + 64i3) + 80i2x * (-1 + -1i + x) + -16i2x2 * (-1 + -1i + x) + 64i3 * (-1 + -1i + x) + -16i3x * (-1 + -1i + x) + 4x2 * (-1 + -1i + x) + -5x3 * (-1 + -1i + x) + x4(-1 + -1i + x))
fx = (4ix2 + -4ix3 + 4i2x2 + -1ix3 + 1ix4 + -1i2x3 + 64i2 + -64i2x + 64i3 + (-1 * 80i2x + -1i * 80i2x + x * 80i2x) + -16i2x2 * (-1 + -1i + x) + 64i3 * (-1 + -1i + x) + -16i3x * (-1 + -1i + x) + 4x2 * (-1 + -1i + x) + -5x3 * (-1 + -1i + x) + x4(-1 + -1i + x))

Reorder the terms:
fx = (4ix2 + -4ix3 + 4i2x2 + -1ix3 + 1ix4 + -1i2x3 + 64i2 + -64i2x + 64i3 + (-80i2x + 80i2x2 + -80i3x) + -16i2x2 * (-1 + -1i + x) + 64i3 * (-1 + -1i + x) + -16i3x * (-1 + -1i + x) + 4x2 * (-1 + -1i + x) + -5x3 * (-1 + -1i + x) + x4(-1 + -1i + x))
fx = (4ix2 + -4ix3 + 4i2x2 + -1ix3 + 1ix4 + -1i2x3 + 64i2 + -64i2x + 64i3 + (-80i2x + 80i2x2 + -80i3x) + -16i2x2 * (-1 + -1i + x) + 64i3 * (-1 + -1i + x) + -16i3x * (-1 + -1i + x) + 4x2 * (-1 + -1i + x) + -5x3 * (-1 + -1i + x) + x4(-1 + -1i + x))
fx = (4ix2 + -4ix3 + 4i2x2 + -1ix3 + 1ix4 + -1i2x3 + 64i2 + -64i2x + 64i3 + -80i2x + 80i2x2 + -80i3x + (-1 * -16i2x2 + -1i * -16i2x2 + x * -16i2x2) + 64i3 * (-1 + -1i + x) + -16i3x * (-1 + -1i + x) + 4x2 * (-1 + -1i + x) + -5x3 * (-1 + -1i + x) + x4(-1 + -1i + x))

Reorder the terms:
fx = (4ix2 + -4ix3 + 4i2x2 + -1ix3 + 1ix4 + -1i2x3 + 64i2 + -64i2x + 64i3 + -80i2x + 80i2x2 + -80i3x + (16i2x2 + -16i2x3 + 16i3x2) + 64i3 * (-1 + -1i + x) + -16i3x * (-1 + -1i + x) + 4x2 * (-1 + -1i + x) + -5x3 * (-1 + -1i + x) + x4(-1 + -1i + x))
fx = (4ix2 + -4ix3 + 4i2x2 + -1ix3 + 1ix4 + -1i2x3 + 64i2 + -64i2x + 64i3 + -80i2x + 80i2x2 + -80i3x + (16i2x2 + -16i2x3 + 16i3x2) + 64i3 * (-1 + -1i + x) + -16i3x * (-1 + -1i + x) + 4x2 * (-1 + -1i + x) + -5x3 * (-1 + -1i + x) + x4(-1 + -1i + x))
fx = (4ix2 + -4ix3 + 4i2x2 + -1ix3 + 1ix4 + -1i2x3 + 64i2 + -64i2x + 64i3 + -80i2x + 80i2x2 + -80i3x + 16i2x2 + -16i2x3 + 16i3x2 + (-1 * 64i3 + -1i * 64i3 + x * 64i3) + -16i3x * (-1 + -1i + x) + 4x2 * (-1 + -1i + x) + -5x3 * (-1 + -1i + x) + x4(-1 + -1i + x))

Reorder the terms:
fx = (4ix2 + -4ix3 + 4i2x2 + -1ix3 + 1ix4 + -1i2x3 + 64i2 + -64i2x + 64i3 + -80i2x + 80i2x2 + -80i3x + 16i2x2 + -16i2x3 + 16i3x2 + (-64i3 + 64i3x + -64i4) + -16i3x * (-1 + -1i + x) + 4x2 * (-1 + -1i + x) + -5x3 * (-1 + -1i + x) + x4(-1 + -1i + x))
fx = (4ix2 + -4ix3 + 4i2x2 + -1ix3 + 1ix4 + -1i2x3 + 64i2 + -64i2x + 64i3 + -80i2x + 80i2x2 + -80i3x + 16i2x2 + -16i2x3 + 16i3x2 + (-64i3 + 64i3x + -64i4) + -16i3x * (-1 + -1i + x) + 4x2 * (-1 + -1i + x) + -5x3 * (-1 + -1i + x) + x4(-1 + -1i + x))
fx = (4ix2 + -4ix3 + 4i2x2 + -1ix3 + 1ix4 + -1i2x3 + 64i2 + -64i2x + 64i3 + -80i2x + 80i2x2 + -80i3x + 16i2x2 + -16i2x3 + 16i3x2 + -64i3 + 64i3x + -64i4 + (-1 * -16i3x + -1i * -16i3x + x * -16i3x) + 4x2 * (-1 + -1i + x) + -5x3 * (-1 + -1i + x) + x4(-1 + -1i + x))

Reorder the terms:
fx = (4ix2 + -4ix3 + 4i2x2 + -1ix3 + 1ix4 + -1i2x3 + 64i2 + -64i2x + 64i3 + -80i2x + 80i2x2 + -80i3x + 16i2x2 + -16i2x3 + 16i3x2 + -64i3 + 64i3x + -64i4 + (16i3x + -16i3x2 + 16i4x) + 4x2 * (-1 + -1i + x) + -5x3 * (-1 + -1i + x) + x4(-1 + -1i + x))
fx = (4ix2 + -4ix3 + 4i2x2 + -1ix3 + 1ix4 + -1i2x3 + 64i2 + -64i2x + 64i3 + -80i2x + 80i2x2 + -80i3x + 16i2x2 + -16i2x3 + 16i3x2 + -64i3 + 64i3x + -64i4 + (16i3x + -16i3x2 + 16i4x) + 4x2 * (-1 + -1i + x) + -5x3 * (-1 + -1i + x) + x4(-1 + -1i + x))
fx = (4ix2 + -4ix3 + 4i2x2 + -1ix3 + 1ix4 + -1i2x3 + 64i2 + -64i2x + 64i3 + -80i2x + 80i2x2 + -80i3x + 16i2x2 + -16i2x3 + 16i3x2 + -64i3 + 64i3x + -64i4 + 16i3x + -16i3x2 + 16i4x + (-1 * 4x2 + -1i * 4x2 + x * 4x2) + -5x3 * (-1 + -1i + x) + x4(-1 + -1i + x))

Reorder the terms:
fx = (4ix2 + -4ix3 + 4i2x2 + -1ix3 + 1ix4 + -1i2x3 + 64i2 + -64i2x + 64i3 + -80i2x + 80i2x2 + -80i3x + 16i2x2 + -16i2x3 + 16i3x2 + -64i3 + 64i3x + -64i4 + 16i3x + -16i3x2 + 16i4x + (-4ix2 + -4x2 + 4x3) + -5x3 * (-1 + -1i + x) + x4(-1 + -1i + x))
fx = (4ix2 + -4ix3 + 4i2x2 + -1ix3 + 1ix4 + -1i2x3 + 64i2 + -64i2x + 64i3 + -80i2x + 80i2x2 + -80i3x + 16i2x2 + -16i2x3 + 16i3x2 + -64i3 + 64i3x + -64i4 + 16i3x + -16i3x2 + 16i4x + (-4ix2 + -4x2 + 4x3) + -5x3 * (-1 + -1i + x) + x4(-1 + -1i + x))
fx = (4ix2 + -4ix3 + 4i2x2 + -1ix3 + 1ix4 + -1i2x3 + 64i2 + -64i2x + 64i3 + -80i2x + 80i2x2 + -80i3x + 16i2x2 + -16i2x3 + 16i3x2 + -64i3 + 64i3x + -64i4 + 16i3x + -16i3x2 + 16i4x + -4ix2 + -4x2 + 4x3 + (-1 * -5x3 + -1i * -5x3 + x * -5x3) + x4(-1 + -1i + x))

Reorder the terms:
fx = (4ix2 + -4ix3 + 4i2x2 + -1ix3 + 1ix4 + -1i2x3 + 64i2 + -64i2x + 64i3 + -80i2x + 80i2x2 + -80i3x + 16i2x2 + -16i2x3 + 16i3x2 + -64i3 + 64i3x + -64i4 + 16i3x + -16i3x2 + 16i4x + -4ix2 + -4x2 + 4x3 + (5ix3 + 5x3 + -5x4) + x4(-1 + -1i + x))
fx = (4ix2 + -4ix3 + 4i2x2 + -1ix3 + 1ix4 + -1i2x3 + 64i2 + -64i2x + 64i3 + -80i2x + 80i2x2 + -80i3x + 16i2x2 + -16i2x3 + 16i3x2 + -64i3 + 64i3x + -64i4 + 16i3x + -16i3x2 + 16i4x + -4ix2 + -4x2 + 4x3 + (5ix3 + 5x3 + -5x4) + x4(-1 + -1i + x))
fx = (4ix2 + -4ix3 + 4i2x2 + -1ix3 + 1ix4 + -1i2x3 + 64i2 + -64i2x + 64i3 + -80i2x + 80i2x2 + -80i3x + 16i2x2 + -16i2x3 + 16i3x2 + -64i3 + 64i3x + -64i4 + 16i3x + -16i3x2 + 16i4x + -4ix2 + -4x2 + 4x3 + 5ix3 + 5x3 + -5x4 + (-1 * x4 + -1i * x4 + x * x4))

Reorder the terms:
fx = (4ix2 + -4ix3 + 4i2x2 + -1ix3 + 1ix4 + -1i2x3 + 64i2 + -64i2x + 64i3 + -80i2x + 80i2x2 + -80i3x + 16i2x2 + -16i2x3 + 16i3x2 + -64i3 + 64i3x + -64i4 + 16i3x + -16i3x2 + 16i4x + -4ix2 + -4x2 + 4x3 + 5ix3 + 5x3 + -5x4 + (-1ix4 + -1x4 + x5))
fx = (4ix2 + -4ix3 + 4i2x2 + -1ix3 + 1ix4 + -1i2x3 + 64i2 + -64i2x + 64i3 + -80i2x + 80i2x2 + -80i3x + 16i2x2 + -16i2x3 + 16i3x2 + -64i3 + 64i3x + -64i4 + 16i3x + -16i3x2 + 16i4x + -4ix2 + -4x2 + 4x3 + 5ix3 + 5x3 + -5x4 + (-1ix4 + -1x4 + x5))

Reorder the terms:
fx = (4ix2 + -4ix2 + -4ix3 + -1ix3 + 5ix3 + 1ix4 + -1ix4 + 64i2 + -64i2x + -80i2x + 4i2x2 + 80i2x2 + 16i2x2 + -1i2x3 + -16i2x3 + 64i3 + -64i3 + -80i3x + 64i3x + 16i3x + 16i3x2 + -16i3x2 + -64i4 + 16i4x + -4x2 + 4x3 + 5x3 + -5x4 + -1x4 + x5)

Combine like terms: 4ix2 + -4ix2 = 0
fx = (0 + -4ix3 + -1ix3 + 5ix3 + 1ix4 + -1ix4 + 64i2 + -64i2x + -80i2x + 4i2x2 + 80i2x2 + 16i2x2 + -1i2x3 + -16i2x3 + 64i3 + -64i3 + -80i3x + 64i3x + 16i3x + 16i3x2 + -16i3x2 + -64i4 + 16i4x + -4x2 + 4x3 + 5x3 + -5x4 + -1x4 + x5)
fx = (-4ix3 + -1ix3 + 5ix3 + 1ix4 + -1ix4 + 64i2 + -64i2x + -80i2x + 4i2x2 + 80i2x2 + 16i2x2 + -1i2x3 + -16i2x3 + 64i3 + -64i3 + -80i3x + 64i3x + 16i3x + 16i3x2 + -16i3x2 + -64i4 + 16i4x + -4x2 + 4x3 + 5x3 + -5x4 + -1x4 + x5)

Combine like terms: -4ix3 + -1ix3 = -5ix3
fx = (-5ix3 + 5ix3 + 1ix4 + -1ix4 + 64i2 + -64i2x + -80i2x + 4i2x2 + 80i2x2 + 16i2x2 + -1i2x3 + -16i2x3 + 64i3 + -64i3 + -80i3x + 64i3x + 16i3x + 16i3x2 + -16i3x2 + -64i4 + 16i4x + -4x2 + 4x3 + 5x3 + -5x4 + -1x4 + x5)

Combine like terms: -5ix3 + 5ix3 = 0
fx = (0 + 1ix4 + -1ix4 + 64i2 + -64i2x + -80i2x + 4i2x2 + 80i2x2 + 16i2x2 + -1i2x3 + -16i2x3 + 64i3 + -64i3 + -80i3x + 64i3x + 16i3x + 16i3x2 + -16i3x2 + -64i4 + 16i4x + -4x2 + 4x3 + 5x3 + -5x4 + -1x4 + x5)
fx = (1ix4 + -1ix4 + 64i2 + -64i2x + -80i2x + 4i2x2 + 80i2x2 + 16i2x2 + -1i2x3 + -16i2x3 + 64i3 + -64i3 + -80i3x + 64i3x + 16i3x + 16i3x2 + -16i3x2 + -64i4 + 16i4x + -4x2 + 4x3 + 5x3 + -5x4 + -1x4 + x5)

Combine like terms: 1ix4 + -1ix4 = 0
fx = (0 + 64i2 + -64i2x + -80i2x + 4i2x2 + 80i2x2 + 16i2x2 + -1i2x3 + -16i2x3 + 64i3 + -64i3 + -80i3x + 64i3x + 16i3x + 16i3x2 + -16i3x2 + -64i4 + 16i4x + -4x2 + 4x3 + 5x3 + -5x4 + -1x4 + x5)
fx = (64i2 + -64i2x + -80i2x + 4i2x2 + 80i2x2 + 16i2x2 + -1i2x3 + -16i2x3 + 64i3 + -64i3 + -80i3x + 64i3x + 16i3x + 16i3x2 + -16i3x2 + -64i4 + 16i4x + -4x2 + 4x3 + 5x3 + -5x4 + -1x4 + x5)

Combine like terms: -64i2x + -80i2x = -144i2x
fx = (64i2 + -144i2x + 4i2x2 + 80i2x2 + 16i2x2 + -1i2x3 + -16i2x3 + 64i3 + -64i3 + -80i3x + 64i3x + 16i3x + 16i3x2 + -16i3x2 + -64i4 + 16i4x + -4x2 + 4x3 + 5x3 + -5x4 + -1x4 + x5)

Combine like terms: 4i2x2 + 80i2x2 = 84i2x2
fx = (64i2 + -144i2x + 84i2x2 + 16i2x2 + -1i2x3 + -16i2x3 + 64i3 + -64i3 + -80i3x + 64i3x + 16i3x + 16i3x2 + -16i3x2 + -64i4 + 16i4x + -4x2 + 4x3 + 5x3 + -5x4 + -1x4 + x5)

Combine like terms: 84i2x2 + 16i2x2 = 100i2x2
fx = (64i2 + -144i2x + 100i2x2 + -1i2x3 + -16i2x3 + 64i3 + -64i3 + -80i3x + 64i3x + 16i3x + 16i3x2 + -16i3x2 + -64i4 + 16i4x + -4x2 + 4x3 + 5x3 + -5x4 + -1x4 + x5)

Combine like terms: -1i2x3 + -16i2x3 = -17i2x3
fx = (64i2 + -144i2x + 100i2x2 + -17i2x3 + 64i3 + -64i3 + -80i3x + 64i3x + 16i3x + 16i3x2 + -16i3x2 + -64i4 + 16i4x + -4x2 + 4x3 + 5x3 + -5x4 + -1x4 + x5)

Combine like terms: 64i3 + -64i3 = 0
fx = (64i2 + -144i2x + 100i2x2 + -17i2x3 + 0 + -80i3x + 64i3x + 16i3x + 16i3x2 + -16i3x2 + -64i4 + 16i4x + -4x2 + 4x3 + 5x3 + -5x4 + -1x4 + x5)
fx = (64i2 + -144i2x + 100i2x2 + -17i2x3 + -80i3x + 64i3x + 16i3x + 16i3x2 + -16i3x2 + -64i4 + 16i4x + -4x2 + 4x3 + 5x3 + -5x4 + -1x4 + x5)

Combine like terms: -80i3x + 64i3x = -16i3x
fx = (64i2 + -144i2x + 100i2x2 + -17i2x3 + -16i3x + 16i3x + 16i3x2 + -16i3x2 + -64i4 + 16i4x + -4x2 + 4x3 + 5x3 + -5x4 + -1x4 + x5)

Combine like terms: -16i3x + 16i3x = 0
fx = (64i2 + -144i2x + 100i2x2 + -17i2x3 + 0 + 16i3x2 + -16i3x2 + -64i4 + 16i4x + -4x2 + 4x3 + 5x3 + -5x4 + -1x4 + x5)
fx = (64i2 + -144i2x + 100i2x2 + -17i2x3 + 16i3x2 + -16i3x2 + -64i4 + 16i4x + -4x2 + 4x3 + 5x3 + -5x4 + -1x4 + x5)

Combine like terms: 16i3x2 + -16i3x2 = 0
fx = (64i2 + -144i2x + 100i2x2 + -17i2x3 + 0 + -64i4 + 16i4x + -4x2 + 4x3 + 5x3 + -5x4 + -1x4 + x5)
fx = (64i2 + -144i2x + 100i2x2 + -17i2x3 + -64i4 + 16i4x + -4x2 + 4x3 + 5x3 + -5x4 + -1x4 + x5)

Combine like terms: 4x3 + 5x3 = 9x3
fx = (64i2 + -144i2x + 100i2x2 + -17i2x3 + -64i4 + 16i4x + -4x2 + 9x3 + -5x4 + -1x4 + x5)

Combine like terms: -5x4 + -1x4 = -6x4
fx = (64i2 + -144i2x + 100i2x2 + -17i2x3 + -64i4 + 16i4x + -4x2 + 9x3 + -6x4 + x5)

Solving
fx = 64i2 + -144i2x + 100i2x2 + -17i2x3 + -64i4 + 16i4x + -4x2 + 9x3 + -6x4 + x5

Solving for variable 'f'.

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

Divide each side by 'x'.
f = 64i2x-1 + -144i2 + 100i2x + -17i2x2 + -64i4x-1 + 16i4 + -4x + 9x2 + -6x3 + x4

Simplifying
f = 64i2x-1 + -144i2 + 100i2x + -17i2x2 + -64i4x-1 + 16i4 + -4x + 9x2 + -6x3 + x4

Reorder the terms:
f = -144i2 + 64i2x-1 + 100i2x + -17i2x2 + 16i4 + -64i4x-1 + -4x + 9x2 + -6x3 + x4

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