f(x)=(x-5)(x-(-3))(x-(-1+3i))(x-(-1-3i))

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Solution for f(x)=(x-5)(x-(-3))(x-(-1+3i))(x-(-1-3i)) equation: 


Simplifying
f(x) = (x + -5)(x + -1(-3))(x + -1(-1 + 3i))(x + -1(-1 + -3i))

Multiply f * x
fx = (x + -5)(x + -1(-3))(x + -1(-1 + 3i))(x + -1(-1 + -3i))

Reorder the terms:
fx = (-5 + x)(x + -1(-3))(x + -1(-1 + 3i))(x + -1(-1 + -3i))

Multiply -1 * -3
fx = (-5 + x)(x + 3)(x + -1(-1 + 3i))(x + -1(-1 + -3i))

Reorder the terms:
fx = (-5 + x)(3 + x)(x + -1(-1 + 3i))(x + -1(-1 + -3i))
fx = (-5 + x)(3 + x)(x + (-1 * -1 + 3i * -1))(x + -1(-1 + -3i))
fx = (-5 + x)(3 + x)(x + (1 + -3i))(x + -1(-1 + -3i))

Reorder the terms:
fx = (-5 + x)(3 + x)(1 + -3i + x)(x + -1(-1 + -3i))
fx = (-5 + x)(3 + x)(1 + -3i + x)(x + (-1 * -1 + -3i * -1))
fx = (-5 + x)(3 + x)(1 + -3i + x)(x + (1 + 3i))

Reorder the terms:
fx = (-5 + x)(3 + x)(1 + -3i + x)(1 + 3i + x)

Multiply (-5 + x) * (3 + x)
fx = (-5(3 + x) + x(3 + x))(1 + -3i + x)(1 + 3i + x)
fx = ((3 * -5 + x * -5) + x(3 + x))(1 + -3i + x)(1 + 3i + x)
fx = ((-15 + -5x) + x(3 + x))(1 + -3i + x)(1 + 3i + x)
fx = (-15 + -5x + (3 * x + x * x))(1 + -3i + x)(1 + 3i + x)
fx = (-15 + -5x + (3x + x2))(1 + -3i + x)(1 + 3i + x)

Combine like terms: -5x + 3x = -2x
fx = (-15 + -2x + x2)(1 + -3i + x)(1 + 3i + x)

Multiply (-15 + -2x + x2) * (1 + -3i + x)
fx = (-15(1 + -3i + x) + -2x * (1 + -3i + x) + x2(1 + -3i + x))(1 + 3i + x)
fx = ((1 * -15 + -3i * -15 + x * -15) + -2x * (1 + -3i + x) + x2(1 + -3i + x))(1 + 3i + x)
fx = ((-15 + 45i + -15x) + -2x * (1 + -3i + x) + x2(1 + -3i + x))(1 + 3i + x)
fx = (-15 + 45i + -15x + (1 * -2x + -3i * -2x + x * -2x) + x2(1 + -3i + x))(1 + 3i + x)

Reorder the terms:
fx = (-15 + 45i + -15x + (6ix + -2x + -2x2) + x2(1 + -3i + x))(1 + 3i + x)
fx = (-15 + 45i + -15x + (6ix + -2x + -2x2) + x2(1 + -3i + x))(1 + 3i + x)
fx = (-15 + 45i + -15x + 6ix + -2x + -2x2 + (1 * x2 + -3i * x2 + x * x2))(1 + 3i + x)

Reorder the terms:
fx = (-15 + 45i + -15x + 6ix + -2x + -2x2 + (-3ix2 + 1x2 + x3))(1 + 3i + x)
fx = (-15 + 45i + -15x + 6ix + -2x + -2x2 + (-3ix2 + 1x2 + x3))(1 + 3i + x)

Reorder the terms:
fx = (-15 + 45i + 6ix + -3ix2 + -15x + -2x + -2x2 + 1x2 + x3)(1 + 3i + x)

Combine like terms: -15x + -2x = -17x
fx = (-15 + 45i + 6ix + -3ix2 + -17x + -2x2 + 1x2 + x3)(1 + 3i + x)

Combine like terms: -2x2 + 1x2 = -1x2
fx = (-15 + 45i + 6ix + -3ix2 + -17x + -1x2 + x3)(1 + 3i + x)

Multiply (-15 + 45i + 6ix + -3ix2 + -17x + -1x2 + x3) * (1 + 3i + x)
fx = (-15(1 + 3i + x) + 45i * (1 + 3i + x) + 6ix * (1 + 3i + x) + -3ix2 * (1 + 3i + x) + -17x * (1 + 3i + x) + -1x2 * (1 + 3i + x) + x3(1 + 3i + x))
fx = ((1 * -15 + 3i * -15 + x * -15) + 45i * (1 + 3i + x) + 6ix * (1 + 3i + x) + -3ix2 * (1 + 3i + x) + -17x * (1 + 3i + x) + -1x2 * (1 + 3i + x) + x3(1 + 3i + x))
fx = ((-15 + -45i + -15x) + 45i * (1 + 3i + x) + 6ix * (1 + 3i + x) + -3ix2 * (1 + 3i + x) + -17x * (1 + 3i + x) + -1x2 * (1 + 3i + x) + x3(1 + 3i + x))
fx = (-15 + -45i + -15x + (1 * 45i + 3i * 45i + x * 45i) + 6ix * (1 + 3i + x) + -3ix2 * (1 + 3i + x) + -17x * (1 + 3i + x) + -1x2 * (1 + 3i + x) + x3(1 + 3i + x))

Reorder the terms:
fx = (-15 + -45i + -15x + (45i + 45ix + 135i2) + 6ix * (1 + 3i + x) + -3ix2 * (1 + 3i + x) + -17x * (1 + 3i + x) + -1x2 * (1 + 3i + x) + x3(1 + 3i + x))
fx = (-15 + -45i + -15x + (45i + 45ix + 135i2) + 6ix * (1 + 3i + x) + -3ix2 * (1 + 3i + x) + -17x * (1 + 3i + x) + -1x2 * (1 + 3i + x) + x3(1 + 3i + x))
fx = (-15 + -45i + -15x + 45i + 45ix + 135i2 + (1 * 6ix + 3i * 6ix + x * 6ix) + -3ix2 * (1 + 3i + x) + -17x * (1 + 3i + x) + -1x2 * (1 + 3i + x) + x3(1 + 3i + x))

Reorder the terms:
fx = (-15 + -45i + -15x + 45i + 45ix + 135i2 + (6ix + 6ix2 + 18i2x) + -3ix2 * (1 + 3i + x) + -17x * (1 + 3i + x) + -1x2 * (1 + 3i + x) + x3(1 + 3i + x))
fx = (-15 + -45i + -15x + 45i + 45ix + 135i2 + (6ix + 6ix2 + 18i2x) + -3ix2 * (1 + 3i + x) + -17x * (1 + 3i + x) + -1x2 * (1 + 3i + x) + x3(1 + 3i + x))
fx = (-15 + -45i + -15x + 45i + 45ix + 135i2 + 6ix + 6ix2 + 18i2x + (1 * -3ix2 + 3i * -3ix2 + x * -3ix2) + -17x * (1 + 3i + x) + -1x2 * (1 + 3i + x) + x3(1 + 3i + x))

Reorder the terms:
fx = (-15 + -45i + -15x + 45i + 45ix + 135i2 + 6ix + 6ix2 + 18i2x + (-3ix2 + -3ix3 + -9i2x2) + -17x * (1 + 3i + x) + -1x2 * (1 + 3i + x) + x3(1 + 3i + x))
fx = (-15 + -45i + -15x + 45i + 45ix + 135i2 + 6ix + 6ix2 + 18i2x + (-3ix2 + -3ix3 + -9i2x2) + -17x * (1 + 3i + x) + -1x2 * (1 + 3i + x) + x3(1 + 3i + x))
fx = (-15 + -45i + -15x + 45i + 45ix + 135i2 + 6ix + 6ix2 + 18i2x + -3ix2 + -3ix3 + -9i2x2 + (1 * -17x + 3i * -17x + x * -17x) + -1x2 * (1 + 3i + x) + x3(1 + 3i + x))

Reorder the terms:
fx = (-15 + -45i + -15x + 45i + 45ix + 135i2 + 6ix + 6ix2 + 18i2x + -3ix2 + -3ix3 + -9i2x2 + (-51ix + -17x + -17x2) + -1x2 * (1 + 3i + x) + x3(1 + 3i + x))
fx = (-15 + -45i + -15x + 45i + 45ix + 135i2 + 6ix + 6ix2 + 18i2x + -3ix2 + -3ix3 + -9i2x2 + (-51ix + -17x + -17x2) + -1x2 * (1 + 3i + x) + x3(1 + 3i + x))
fx = (-15 + -45i + -15x + 45i + 45ix + 135i2 + 6ix + 6ix2 + 18i2x + -3ix2 + -3ix3 + -9i2x2 + -51ix + -17x + -17x2 + (1 * -1x2 + 3i * -1x2 + x * -1x2) + x3(1 + 3i + x))

Reorder the terms:
fx = (-15 + -45i + -15x + 45i + 45ix + 135i2 + 6ix + 6ix2 + 18i2x + -3ix2 + -3ix3 + -9i2x2 + -51ix + -17x + -17x2 + (-3ix2 + -1x2 + -1x3) + x3(1 + 3i + x))
fx = (-15 + -45i + -15x + 45i + 45ix + 135i2 + 6ix + 6ix2 + 18i2x + -3ix2 + -3ix3 + -9i2x2 + -51ix + -17x + -17x2 + (-3ix2 + -1x2 + -1x3) + x3(1 + 3i + x))
fx = (-15 + -45i + -15x + 45i + 45ix + 135i2 + 6ix + 6ix2 + 18i2x + -3ix2 + -3ix3 + -9i2x2 + -51ix + -17x + -17x2 + -3ix2 + -1x2 + -1x3 + (1 * x3 + 3i * x3 + x * x3))

Reorder the terms:
fx = (-15 + -45i + -15x + 45i + 45ix + 135i2 + 6ix + 6ix2 + 18i2x + -3ix2 + -3ix3 + -9i2x2 + -51ix + -17x + -17x2 + -3ix2 + -1x2 + -1x3 + (3ix3 + 1x3 + x4))
fx = (-15 + -45i + -15x + 45i + 45ix + 135i2 + 6ix + 6ix2 + 18i2x + -3ix2 + -3ix3 + -9i2x2 + -51ix + -17x + -17x2 + -3ix2 + -1x2 + -1x3 + (3ix3 + 1x3 + x4))

Reorder the terms:
fx = (-15 + -45i + 45i + 45ix + 6ix + -51ix + 6ix2 + -3ix2 + -3ix2 + -3ix3 + 3ix3 + 135i2 + 18i2x + -9i2x2 + -15x + -17x + -17x2 + -1x2 + -1x3 + 1x3 + x4)

Combine like terms: -45i + 45i = 0
fx = (-15 + 0 + 45ix + 6ix + -51ix + 6ix2 + -3ix2 + -3ix2 + -3ix3 + 3ix3 + 135i2 + 18i2x + -9i2x2 + -15x + -17x + -17x2 + -1x2 + -1x3 + 1x3 + x4)
fx = (-15 + 45ix + 6ix + -51ix + 6ix2 + -3ix2 + -3ix2 + -3ix3 + 3ix3 + 135i2 + 18i2x + -9i2x2 + -15x + -17x + -17x2 + -1x2 + -1x3 + 1x3 + x4)

Combine like terms: 45ix + 6ix = 51ix
fx = (-15 + 51ix + -51ix + 6ix2 + -3ix2 + -3ix2 + -3ix3 + 3ix3 + 135i2 + 18i2x + -9i2x2 + -15x + -17x + -17x2 + -1x2 + -1x3 + 1x3 + x4)

Combine like terms: 51ix + -51ix = 0
fx = (-15 + 0 + 6ix2 + -3ix2 + -3ix2 + -3ix3 + 3ix3 + 135i2 + 18i2x + -9i2x2 + -15x + -17x + -17x2 + -1x2 + -1x3 + 1x3 + x4)
fx = (-15 + 6ix2 + -3ix2 + -3ix2 + -3ix3 + 3ix3 + 135i2 + 18i2x + -9i2x2 + -15x + -17x + -17x2 + -1x2 + -1x3 + 1x3 + x4)

Combine like terms: 6ix2 + -3ix2 = 3ix2
fx = (-15 + 3ix2 + -3ix2 + -3ix3 + 3ix3 + 135i2 + 18i2x + -9i2x2 + -15x + -17x + -17x2 + -1x2 + -1x3 + 1x3 + x4)

Combine like terms: 3ix2 + -3ix2 = 0
fx = (-15 + 0 + -3ix3 + 3ix3 + 135i2 + 18i2x + -9i2x2 + -15x + -17x + -17x2 + -1x2 + -1x3 + 1x3 + x4)
fx = (-15 + -3ix3 + 3ix3 + 135i2 + 18i2x + -9i2x2 + -15x + -17x + -17x2 + -1x2 + -1x3 + 1x3 + x4)

Combine like terms: -3ix3 + 3ix3 = 0
fx = (-15 + 0 + 135i2 + 18i2x + -9i2x2 + -15x + -17x + -17x2 + -1x2 + -1x3 + 1x3 + x4)
fx = (-15 + 135i2 + 18i2x + -9i2x2 + -15x + -17x + -17x2 + -1x2 + -1x3 + 1x3 + x4)

Combine like terms: -15x + -17x = -32x
fx = (-15 + 135i2 + 18i2x + -9i2x2 + -32x + -17x2 + -1x2 + -1x3 + 1x3 + x4)

Combine like terms: -17x2 + -1x2 = -18x2
fx = (-15 + 135i2 + 18i2x + -9i2x2 + -32x + -18x2 + -1x3 + 1x3 + x4)

Combine like terms: -1x3 + 1x3 = 0
fx = (-15 + 135i2 + 18i2x + -9i2x2 + -32x + -18x2 + 0 + x4)
fx = (-15 + 135i2 + 18i2x + -9i2x2 + -32x + -18x2 + x4)

Solving
fx = -15 + 135i2 + 18i2x + -9i2x2 + -32x + -18x2 + 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 = -15x-1 + 135i2x-1 + 18i2 + -9i2x + -32 + -18x + x3

Simplifying
f = -15x-1 + 135i2x-1 + 18i2 + -9i2x + -32 + -18x + x3

Reorder the terms:
f = -32 + 18i2 + 135i2x-1 + -9i2x + -15x-1 + -18x + x3

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