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

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


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

Multiply f * x
fx = an(x + 2)(x + -4 + -4i)(x + -4 + 4i)

Reorder the terms:
fx = an(2 + x)(x + -4 + -4i)(x + -4 + 4i)

Reorder the terms:
fx = an(2 + x)(-4 + -4i + x)(x + -4 + 4i)

Reorder the terms:
fx = an(2 + x)(-4 + -4i + x)(-4 + 4i + x)

Multiply (2 + x) * (-4 + -4i + x)
fx = an(2(-4 + -4i + x) + x(-4 + -4i + x))(-4 + 4i + x)
fx = an((-4 * 2 + -4i * 2 + x * 2) + x(-4 + -4i + x))(-4 + 4i + x)
fx = an((-8 + -8i + 2x) + x(-4 + -4i + x))(-4 + 4i + x)
fx = an(-8 + -8i + 2x + (-4 * x + -4i * x + x * x))(-4 + 4i + x)

Reorder the terms:
fx = an(-8 + -8i + 2x + (-4ix + -4x + x2))(-4 + 4i + x)
fx = an(-8 + -8i + 2x + (-4ix + -4x + x2))(-4 + 4i + x)

Reorder the terms:
fx = an(-8 + -8i + -4ix + 2x + -4x + x2)(-4 + 4i + x)

Combine like terms: 2x + -4x = -2x
fx = an(-8 + -8i + -4ix + -2x + x2)(-4 + 4i + x)

Multiply (-8 + -8i + -4ix + -2x + x2) * (-4 + 4i + x)
fx = an(-8(-4 + 4i + x) + -8i * (-4 + 4i + x) + -4ix * (-4 + 4i + x) + -2x * (-4 + 4i + x) + x2(-4 + 4i + x))
fx = an((-4 * -8 + 4i * -8 + x * -8) + -8i * (-4 + 4i + x) + -4ix * (-4 + 4i + x) + -2x * (-4 + 4i + x) + x2(-4 + 4i + x))
fx = an((32 + -32i + -8x) + -8i * (-4 + 4i + x) + -4ix * (-4 + 4i + x) + -2x * (-4 + 4i + x) + x2(-4 + 4i + x))
fx = an(32 + -32i + -8x + (-4 * -8i + 4i * -8i + x * -8i) + -4ix * (-4 + 4i + x) + -2x * (-4 + 4i + x) + x2(-4 + 4i + x))

Reorder the terms:
fx = an(32 + -32i + -8x + (32i + -8ix + -32i2) + -4ix * (-4 + 4i + x) + -2x * (-4 + 4i + x) + x2(-4 + 4i + x))
fx = an(32 + -32i + -8x + (32i + -8ix + -32i2) + -4ix * (-4 + 4i + x) + -2x * (-4 + 4i + x) + x2(-4 + 4i + x))
fx = an(32 + -32i + -8x + 32i + -8ix + -32i2 + (-4 * -4ix + 4i * -4ix + x * -4ix) + -2x * (-4 + 4i + x) + x2(-4 + 4i + x))

Reorder the terms:
fx = an(32 + -32i + -8x + 32i + -8ix + -32i2 + (16ix + -4ix2 + -16i2x) + -2x * (-4 + 4i + x) + x2(-4 + 4i + x))
fx = an(32 + -32i + -8x + 32i + -8ix + -32i2 + (16ix + -4ix2 + -16i2x) + -2x * (-4 + 4i + x) + x2(-4 + 4i + x))
fx = an(32 + -32i + -8x + 32i + -8ix + -32i2 + 16ix + -4ix2 + -16i2x + (-4 * -2x + 4i * -2x + x * -2x) + x2(-4 + 4i + x))

Reorder the terms:
fx = an(32 + -32i + -8x + 32i + -8ix + -32i2 + 16ix + -4ix2 + -16i2x + (-8ix + 8x + -2x2) + x2(-4 + 4i + x))
fx = an(32 + -32i + -8x + 32i + -8ix + -32i2 + 16ix + -4ix2 + -16i2x + (-8ix + 8x + -2x2) + x2(-4 + 4i + x))
fx = an(32 + -32i + -8x + 32i + -8ix + -32i2 + 16ix + -4ix2 + -16i2x + -8ix + 8x + -2x2 + (-4 * x2 + 4i * x2 + x * x2))

Reorder the terms:
fx = an(32 + -32i + -8x + 32i + -8ix + -32i2 + 16ix + -4ix2 + -16i2x + -8ix + 8x + -2x2 + (4ix2 + -4x2 + x3))
fx = an(32 + -32i + -8x + 32i + -8ix + -32i2 + 16ix + -4ix2 + -16i2x + -8ix + 8x + -2x2 + (4ix2 + -4x2 + x3))

Reorder the terms:
fx = an(32 + -32i + 32i + -8ix + 16ix + -8ix + -4ix2 + 4ix2 + -32i2 + -16i2x + -8x + 8x + -2x2 + -4x2 + x3)

Combine like terms: -32i + 32i = 0
fx = an(32 + 0 + -8ix + 16ix + -8ix + -4ix2 + 4ix2 + -32i2 + -16i2x + -8x + 8x + -2x2 + -4x2 + x3)
fx = an(32 + -8ix + 16ix + -8ix + -4ix2 + 4ix2 + -32i2 + -16i2x + -8x + 8x + -2x2 + -4x2 + x3)

Combine like terms: -8ix + 16ix = 8ix
fx = an(32 + 8ix + -8ix + -4ix2 + 4ix2 + -32i2 + -16i2x + -8x + 8x + -2x2 + -4x2 + x3)

Combine like terms: 8ix + -8ix = 0
fx = an(32 + 0 + -4ix2 + 4ix2 + -32i2 + -16i2x + -8x + 8x + -2x2 + -4x2 + x3)
fx = an(32 + -4ix2 + 4ix2 + -32i2 + -16i2x + -8x + 8x + -2x2 + -4x2 + x3)

Combine like terms: -4ix2 + 4ix2 = 0
fx = an(32 + 0 + -32i2 + -16i2x + -8x + 8x + -2x2 + -4x2 + x3)
fx = an(32 + -32i2 + -16i2x + -8x + 8x + -2x2 + -4x2 + x3)

Combine like terms: -8x + 8x = 0
fx = an(32 + -32i2 + -16i2x + 0 + -2x2 + -4x2 + x3)
fx = an(32 + -32i2 + -16i2x + -2x2 + -4x2 + x3)

Combine like terms: -2x2 + -4x2 = -6x2
fx = an(32 + -32i2 + -16i2x + -6x2 + x3)
fx = (32 * an + -32i2 * an + -16i2x * an + -6x2 * an + x3 * an)

Reorder the terms:
fx = (-32ai2n + -16ai2nx + 32an + -6anx2 + anx3)
fx = (-32ai2n + -16ai2nx + 32an + -6anx2 + anx3)

Solving
fx = -32ai2n + -16ai2nx + 32an + -6anx2 + anx3

Solving for variable 'f'.

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

Divide each side by 'x'.
f = -32ai2nx-1 + -16ai2n + 32anx-1 + -6anx + anx2

Simplifying
f = -32ai2nx-1 + -16ai2n + 32anx-1 + -6anx + anx2

Reorder the terms:
f = -16ai2n + -32ai2nx-1 + 32anx-1 + -6anx + anx2

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