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

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


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

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

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

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

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

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

Reorder the terms:
fx = ((-4ix + ix2 + 1i2x) + 4x * (-4 + 1i + x))(-4 + x)
fx = ((-4ix + ix2 + 1i2x) + 4x * (-4 + 1i + x))(-4 + x)
fx = (-4ix + ix2 + 1i2x + (-4 * 4x + 1i * 4x + x * 4x))(-4 + x)

Reorder the terms:
fx = (-4ix + ix2 + 1i2x + (4ix + -16x + 4x2))(-4 + x)
fx = (-4ix + ix2 + 1i2x + (4ix + -16x + 4x2))(-4 + x)

Reorder the terms:
fx = (-4ix + 4ix + ix2 + 1i2x + -16x + 4x2)(-4 + x)

Combine like terms: -4ix + 4ix = 0
fx = (0 + ix2 + 1i2x + -16x + 4x2)(-4 + x)
fx = (ix2 + 1i2x + -16x + 4x2)(-4 + x)

Multiply (ix2 + 1i2x + -16x + 4x2) * (-4 + x)
fx = (ix2(-4 + x) + 1i2x * (-4 + x) + -16x * (-4 + x) + 4x2 * (-4 + x))
fx = ((-4 * ix2 + x * ix2) + 1i2x * (-4 + x) + -16x * (-4 + x) + 4x2 * (-4 + x))
fx = ((-4ix2 + ix3) + 1i2x * (-4 + x) + -16x * (-4 + x) + 4x2 * (-4 + x))
fx = (-4ix2 + ix3 + (-4 * 1i2x + x * 1i2x) + -16x * (-4 + x) + 4x2 * (-4 + x))
fx = (-4ix2 + ix3 + (-4i2x + 1i2x2) + -16x * (-4 + x) + 4x2 * (-4 + x))
fx = (-4ix2 + ix3 + -4i2x + 1i2x2 + (-4 * -16x + x * -16x) + 4x2 * (-4 + x))
fx = (-4ix2 + ix3 + -4i2x + 1i2x2 + (64x + -16x2) + 4x2 * (-4 + x))
fx = (-4ix2 + ix3 + -4i2x + 1i2x2 + 64x + -16x2 + (-4 * 4x2 + x * 4x2))
fx = (-4ix2 + ix3 + -4i2x + 1i2x2 + 64x + -16x2 + (-16x2 + 4x3))

Combine like terms: -16x2 + -16x2 = -32x2
fx = (-4ix2 + ix3 + -4i2x + 1i2x2 + 64x + -32x2 + 4x3)

Solving
fx = -4ix2 + ix3 + -4i2x + 1i2x2 + 64x + -32x2 + 4x3

Solving for variable 'f'.

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

Divide each side by 'x'.
f = -4ix + ix2 + -4i2 + i2x + 64 + -32x + 4x2

Simplifying
f = -4ix + ix2 + -4i2 + i2x + 64 + -32x + 4x2

Reorder the terms:
f = 64 + -4ix + ix2 + -4i2 + i2x + -32x + 4x2

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