f(x)=(x+2)(x-1)[x-(4+3i)][x-(4-3i)]

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Solution for f(x)=(x+2)(x-1)[x-(4+3i)][x-(4-3i)] equation: 


Simplifying
f(x) = (x + 2)(x + -1)[x + -1(4 + 3i)][x + -1(4 + -3i)]

Multiply f * x
fx = (x + 2)(x + -1)[x + -1(4 + 3i)][x + -1(4 + -3i)]

Reorder the terms:
fx = (2 + x)(x + -1)[x + -1(4 + 3i)][x + -1(4 + -3i)]

Reorder the terms:
fx = (2 + x)(-1 + x)[x + -1(4 + 3i)][x + -1(4 + -3i)]
fx = (2 + x)(-1 + x)[x + (4 * -1 + 3i * -1)][x + -1(4 + -3i)]
fx = (2 + x)(-1 + x)[x + (-4 + -3i)][x + -1(4 + -3i)]

Reorder the terms:
fx = (2 + x)(-1 + x)[-4 + -3i + x][x + -1(4 + -3i)]
fx = (2 + x)(-1 + x)[-4 + -3i + x][x + (4 * -1 + -3i * -1)]
fx = (2 + x)(-1 + x)[-4 + -3i + x][x + (-4 + 3i)]

Reorder the terms:
fx = (2 + x)(-1 + x)[-4 + -3i + x][-4 + 3i + x]

Multiply (2 + x) * (-1 + x)
fx = (2(-1 + x) + x(-1 + x))[-4 + -3i + x][-4 + 3i + x]
fx = ((-1 * 2 + x * 2) + x(-1 + x))[-4 + -3i + x][-4 + 3i + x]
fx = ((-2 + 2x) + x(-1 + x))[-4 + -3i + x][-4 + 3i + x]
fx = (-2 + 2x + (-1 * x + x * x))[-4 + -3i + x][-4 + 3i + x]
fx = (-2 + 2x + (-1x + x2))[-4 + -3i + x][-4 + 3i + x]

Combine like terms: 2x + -1x = 1x
fx = (-2 + 1x + x2)[-4 + -3i + x][-4 + 3i + x]

Multiply (-2 + 1x + x2) * [-4 + -3i + x]
fx = (-2[-4 + -3i + x] + 1x * [-4 + -3i + x] + x2[-4 + -3i + x])[-4 + 3i + x]
fx = ([-4 * -2 + -3i * -2 + x * -2] + 1x * [-4 + -3i + x] + x2[-4 + -3i + x])[-4 + 3i + x]
fx = ([8 + 6i + -2x] + 1x * [-4 + -3i + x] + x2[-4 + -3i + x])[-4 + 3i + x]
fx = (8 + 6i + -2x + [-4 * 1x + -3i * 1x + x * 1x] + x2[-4 + -3i + x])[-4 + 3i + x]

Reorder the terms:
fx = (8 + 6i + -2x + [-3ix + -4x + 1x2] + x2[-4 + -3i + x])[-4 + 3i + x]
fx = (8 + 6i + -2x + [-3ix + -4x + 1x2] + x2[-4 + -3i + x])[-4 + 3i + x]
fx = (8 + 6i + -2x + -3ix + -4x + 1x2 + [-4 * x2 + -3i * x2 + x * x2])[-4 + 3i + x]

Reorder the terms:
fx = (8 + 6i + -2x + -3ix + -4x + 1x2 + [-3ix2 + -4x2 + x3])[-4 + 3i + x]
fx = (8 + 6i + -2x + -3ix + -4x + 1x2 + [-3ix2 + -4x2 + x3])[-4 + 3i + x]

Reorder the terms:
fx = (8 + 6i + -3ix + -3ix2 + -2x + -4x + 1x2 + -4x2 + x3)[-4 + 3i + x]

Combine like terms: -2x + -4x = -6x
fx = (8 + 6i + -3ix + -3ix2 + -6x + 1x2 + -4x2 + x3)[-4 + 3i + x]

Combine like terms: 1x2 + -4x2 = -3x2
fx = (8 + 6i + -3ix + -3ix2 + -6x + -3x2 + x3)[-4 + 3i + x]

Multiply (8 + 6i + -3ix + -3ix2 + -6x + -3x2 + x3) * [-4 + 3i + x]
fx = (8[-4 + 3i + x] + 6i * [-4 + 3i + x] + -3ix * [-4 + 3i + x] + -3ix2 * [-4 + 3i + x] + -6x * [-4 + 3i + x] + -3x2 * [-4 + 3i + x] + x3[-4 + 3i + x])
fx = ([-4 * 8 + 3i * 8 + x * 8] + 6i * [-4 + 3i + x] + -3ix * [-4 + 3i + x] + -3ix2 * [-4 + 3i + x] + -6x * [-4 + 3i + x] + -3x2 * [-4 + 3i + x] + x3[-4 + 3i + x])
fx = ([-32 + 24i + 8x] + 6i * [-4 + 3i + x] + -3ix * [-4 + 3i + x] + -3ix2 * [-4 + 3i + x] + -6x * [-4 + 3i + x] + -3x2 * [-4 + 3i + x] + x3[-4 + 3i + x])
fx = (-32 + 24i + 8x + [-4 * 6i + 3i * 6i + x * 6i] + -3ix * [-4 + 3i + x] + -3ix2 * [-4 + 3i + x] + -6x * [-4 + 3i + x] + -3x2 * [-4 + 3i + x] + x3[-4 + 3i + x])

Reorder the terms:
fx = (-32 + 24i + 8x + [-24i + 6ix + 18i2] + -3ix * [-4 + 3i + x] + -3ix2 * [-4 + 3i + x] + -6x * [-4 + 3i + x] + -3x2 * [-4 + 3i + x] + x3[-4 + 3i + x])
fx = (-32 + 24i + 8x + [-24i + 6ix + 18i2] + -3ix * [-4 + 3i + x] + -3ix2 * [-4 + 3i + x] + -6x * [-4 + 3i + x] + -3x2 * [-4 + 3i + x] + x3[-4 + 3i + x])
fx = (-32 + 24i + 8x + -24i + 6ix + 18i2 + [-4 * -3ix + 3i * -3ix + x * -3ix] + -3ix2 * [-4 + 3i + x] + -6x * [-4 + 3i + x] + -3x2 * [-4 + 3i + x] + x3[-4 + 3i + x])

Reorder the terms:
fx = (-32 + 24i + 8x + -24i + 6ix + 18i2 + [12ix + -3ix2 + -9i2x] + -3ix2 * [-4 + 3i + x] + -6x * [-4 + 3i + x] + -3x2 * [-4 + 3i + x] + x3[-4 + 3i + x])
fx = (-32 + 24i + 8x + -24i + 6ix + 18i2 + [12ix + -3ix2 + -9i2x] + -3ix2 * [-4 + 3i + x] + -6x * [-4 + 3i + x] + -3x2 * [-4 + 3i + x] + x3[-4 + 3i + x])
fx = (-32 + 24i + 8x + -24i + 6ix + 18i2 + 12ix + -3ix2 + -9i2x + [-4 * -3ix2 + 3i * -3ix2 + x * -3ix2] + -6x * [-4 + 3i + x] + -3x2 * [-4 + 3i + x] + x3[-4 + 3i + x])

Reorder the terms:
fx = (-32 + 24i + 8x + -24i + 6ix + 18i2 + 12ix + -3ix2 + -9i2x + [12ix2 + -3ix3 + -9i2x2] + -6x * [-4 + 3i + x] + -3x2 * [-4 + 3i + x] + x3[-4 + 3i + x])
fx = (-32 + 24i + 8x + -24i + 6ix + 18i2 + 12ix + -3ix2 + -9i2x + [12ix2 + -3ix3 + -9i2x2] + -6x * [-4 + 3i + x] + -3x2 * [-4 + 3i + x] + x3[-4 + 3i + x])
fx = (-32 + 24i + 8x + -24i + 6ix + 18i2 + 12ix + -3ix2 + -9i2x + 12ix2 + -3ix3 + -9i2x2 + [-4 * -6x + 3i * -6x + x * -6x] + -3x2 * [-4 + 3i + x] + x3[-4 + 3i + x])

Reorder the terms:
fx = (-32 + 24i + 8x + -24i + 6ix + 18i2 + 12ix + -3ix2 + -9i2x + 12ix2 + -3ix3 + -9i2x2 + [-18ix + 24x + -6x2] + -3x2 * [-4 + 3i + x] + x3[-4 + 3i + x])
fx = (-32 + 24i + 8x + -24i + 6ix + 18i2 + 12ix + -3ix2 + -9i2x + 12ix2 + -3ix3 + -9i2x2 + [-18ix + 24x + -6x2] + -3x2 * [-4 + 3i + x] + x3[-4 + 3i + x])
fx = (-32 + 24i + 8x + -24i + 6ix + 18i2 + 12ix + -3ix2 + -9i2x + 12ix2 + -3ix3 + -9i2x2 + -18ix + 24x + -6x2 + [-4 * -3x2 + 3i * -3x2 + x * -3x2] + x3[-4 + 3i + x])

Reorder the terms:
fx = (-32 + 24i + 8x + -24i + 6ix + 18i2 + 12ix + -3ix2 + -9i2x + 12ix2 + -3ix3 + -9i2x2 + -18ix + 24x + -6x2 + [-9ix2 + 12x2 + -3x3] + x3[-4 + 3i + x])
fx = (-32 + 24i + 8x + -24i + 6ix + 18i2 + 12ix + -3ix2 + -9i2x + 12ix2 + -3ix3 + -9i2x2 + -18ix + 24x + -6x2 + [-9ix2 + 12x2 + -3x3] + x3[-4 + 3i + x])
fx = (-32 + 24i + 8x + -24i + 6ix + 18i2 + 12ix + -3ix2 + -9i2x + 12ix2 + -3ix3 + -9i2x2 + -18ix + 24x + -6x2 + -9ix2 + 12x2 + -3x3 + [-4 * x3 + 3i * x3 + x * x3])

Reorder the terms:
fx = (-32 + 24i + 8x + -24i + 6ix + 18i2 + 12ix + -3ix2 + -9i2x + 12ix2 + -3ix3 + -9i2x2 + -18ix + 24x + -6x2 + -9ix2 + 12x2 + -3x3 + [3ix3 + -4x3 + x4])
fx = (-32 + 24i + 8x + -24i + 6ix + 18i2 + 12ix + -3ix2 + -9i2x + 12ix2 + -3ix3 + -9i2x2 + -18ix + 24x + -6x2 + -9ix2 + 12x2 + -3x3 + [3ix3 + -4x3 + x4])

Reorder the terms:
fx = (-32 + 24i + -24i + 6ix + 12ix + -18ix + -3ix2 + 12ix2 + -9ix2 + -3ix3 + 3ix3 + 18i2 + -9i2x + -9i2x2 + 8x + 24x + -6x2 + 12x2 + -3x3 + -4x3 + x4)

Combine like terms: 24i + -24i = 0
fx = (-32 + 0 + 6ix + 12ix + -18ix + -3ix2 + 12ix2 + -9ix2 + -3ix3 + 3ix3 + 18i2 + -9i2x + -9i2x2 + 8x + 24x + -6x2 + 12x2 + -3x3 + -4x3 + x4)
fx = (-32 + 6ix + 12ix + -18ix + -3ix2 + 12ix2 + -9ix2 + -3ix3 + 3ix3 + 18i2 + -9i2x + -9i2x2 + 8x + 24x + -6x2 + 12x2 + -3x3 + -4x3 + x4)

Combine like terms: 6ix + 12ix = 18ix
fx = (-32 + 18ix + -18ix + -3ix2 + 12ix2 + -9ix2 + -3ix3 + 3ix3 + 18i2 + -9i2x + -9i2x2 + 8x + 24x + -6x2 + 12x2 + -3x3 + -4x3 + x4)

Combine like terms: 18ix + -18ix = 0
fx = (-32 + 0 + -3ix2 + 12ix2 + -9ix2 + -3ix3 + 3ix3 + 18i2 + -9i2x + -9i2x2 + 8x + 24x + -6x2 + 12x2 + -3x3 + -4x3 + x4)
fx = (-32 + -3ix2 + 12ix2 + -9ix2 + -3ix3 + 3ix3 + 18i2 + -9i2x + -9i2x2 + 8x + 24x + -6x2 + 12x2 + -3x3 + -4x3 + x4)

Combine like terms: -3ix2 + 12ix2 = 9ix2
fx = (-32 + 9ix2 + -9ix2 + -3ix3 + 3ix3 + 18i2 + -9i2x + -9i2x2 + 8x + 24x + -6x2 + 12x2 + -3x3 + -4x3 + x4)

Combine like terms: 9ix2 + -9ix2 = 0
fx = (-32 + 0 + -3ix3 + 3ix3 + 18i2 + -9i2x + -9i2x2 + 8x + 24x + -6x2 + 12x2 + -3x3 + -4x3 + x4)
fx = (-32 + -3ix3 + 3ix3 + 18i2 + -9i2x + -9i2x2 + 8x + 24x + -6x2 + 12x2 + -3x3 + -4x3 + x4)

Combine like terms: -3ix3 + 3ix3 = 0
fx = (-32 + 0 + 18i2 + -9i2x + -9i2x2 + 8x + 24x + -6x2 + 12x2 + -3x3 + -4x3 + x4)
fx = (-32 + 18i2 + -9i2x + -9i2x2 + 8x + 24x + -6x2 + 12x2 + -3x3 + -4x3 + x4)

Combine like terms: 8x + 24x = 32x
fx = (-32 + 18i2 + -9i2x + -9i2x2 + 32x + -6x2 + 12x2 + -3x3 + -4x3 + x4)

Combine like terms: -6x2 + 12x2 = 6x2
fx = (-32 + 18i2 + -9i2x + -9i2x2 + 32x + 6x2 + -3x3 + -4x3 + x4)

Combine like terms: -3x3 + -4x3 = -7x3
fx = (-32 + 18i2 + -9i2x + -9i2x2 + 32x + 6x2 + -7x3 + x4)

Solving
fx = -32 + 18i2 + -9i2x + -9i2x2 + 32x + 6x2 + -7x3 + x4

Solving for variable 'f'.

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

Divide each side by 'x'.
f = -32x-1 + 18i2x-1 + -9i2 + -9i2x + 32 + 6x + -7x2 + x3

Simplifying
f = -32x-1 + 18i2x-1 + -9i2 + -9i2x + 32 + 6x + -7x2 + x3

Reorder the terms:
f = 32 + -9i2 + 18i2x-1 + -9i2x + -32x-1 + 6x + -7x2 + x3

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