f(x)=(x-4)(x-(-1+3i))(x-(-1-3i))

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


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

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

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

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

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

Multiply (-4 + x) * (1 + -3i + x)
fx = (-4(1 + -3i + x) + x(1 + -3i + x))(1 + 3i + x)
fx = ((1 * -4 + -3i * -4 + x * -4) + x(1 + -3i + x))(1 + 3i + x)
fx = ((-4 + 12i + -4x) + x(1 + -3i + x))(1 + 3i + x)
fx = (-4 + 12i + -4x + (1 * x + -3i * x + x * x))(1 + 3i + x)

Reorder the terms:
fx = (-4 + 12i + -4x + (-3ix + 1x + x2))(1 + 3i + x)
fx = (-4 + 12i + -4x + (-3ix + 1x + x2))(1 + 3i + x)

Reorder the terms:
fx = (-4 + 12i + -3ix + -4x + 1x + x2)(1 + 3i + x)

Combine like terms: -4x + 1x = -3x
fx = (-4 + 12i + -3ix + -3x + x2)(1 + 3i + x)

Multiply (-4 + 12i + -3ix + -3x + x2) * (1 + 3i + x)
fx = (-4(1 + 3i + x) + 12i * (1 + 3i + x) + -3ix * (1 + 3i + x) + -3x * (1 + 3i + x) + x2(1 + 3i + x))
fx = ((1 * -4 + 3i * -4 + x * -4) + 12i * (1 + 3i + x) + -3ix * (1 + 3i + x) + -3x * (1 + 3i + x) + x2(1 + 3i + x))
fx = ((-4 + -12i + -4x) + 12i * (1 + 3i + x) + -3ix * (1 + 3i + x) + -3x * (1 + 3i + x) + x2(1 + 3i + x))
fx = (-4 + -12i + -4x + (1 * 12i + 3i * 12i + x * 12i) + -3ix * (1 + 3i + x) + -3x * (1 + 3i + x) + x2(1 + 3i + x))

Reorder the terms:
fx = (-4 + -12i + -4x + (12i + 12ix + 36i2) + -3ix * (1 + 3i + x) + -3x * (1 + 3i + x) + x2(1 + 3i + x))
fx = (-4 + -12i + -4x + (12i + 12ix + 36i2) + -3ix * (1 + 3i + x) + -3x * (1 + 3i + x) + x2(1 + 3i + x))
fx = (-4 + -12i + -4x + 12i + 12ix + 36i2 + (1 * -3ix + 3i * -3ix + x * -3ix) + -3x * (1 + 3i + x) + x2(1 + 3i + x))

Reorder the terms:
fx = (-4 + -12i + -4x + 12i + 12ix + 36i2 + (-3ix + -3ix2 + -9i2x) + -3x * (1 + 3i + x) + x2(1 + 3i + x))
fx = (-4 + -12i + -4x + 12i + 12ix + 36i2 + (-3ix + -3ix2 + -9i2x) + -3x * (1 + 3i + x) + x2(1 + 3i + x))
fx = (-4 + -12i + -4x + 12i + 12ix + 36i2 + -3ix + -3ix2 + -9i2x + (1 * -3x + 3i * -3x + x * -3x) + x2(1 + 3i + x))

Reorder the terms:
fx = (-4 + -12i + -4x + 12i + 12ix + 36i2 + -3ix + -3ix2 + -9i2x + (-9ix + -3x + -3x2) + x2(1 + 3i + x))
fx = (-4 + -12i + -4x + 12i + 12ix + 36i2 + -3ix + -3ix2 + -9i2x + (-9ix + -3x + -3x2) + x2(1 + 3i + x))
fx = (-4 + -12i + -4x + 12i + 12ix + 36i2 + -3ix + -3ix2 + -9i2x + -9ix + -3x + -3x2 + (1 * x2 + 3i * x2 + x * x2))

Reorder the terms:
fx = (-4 + -12i + -4x + 12i + 12ix + 36i2 + -3ix + -3ix2 + -9i2x + -9ix + -3x + -3x2 + (3ix2 + 1x2 + x3))
fx = (-4 + -12i + -4x + 12i + 12ix + 36i2 + -3ix + -3ix2 + -9i2x + -9ix + -3x + -3x2 + (3ix2 + 1x2 + x3))

Reorder the terms:
fx = (-4 + -12i + 12i + 12ix + -3ix + -9ix + -3ix2 + 3ix2 + 36i2 + -9i2x + -4x + -3x + -3x2 + 1x2 + x3)

Combine like terms: -12i + 12i = 0
fx = (-4 + 0 + 12ix + -3ix + -9ix + -3ix2 + 3ix2 + 36i2 + -9i2x + -4x + -3x + -3x2 + 1x2 + x3)
fx = (-4 + 12ix + -3ix + -9ix + -3ix2 + 3ix2 + 36i2 + -9i2x + -4x + -3x + -3x2 + 1x2 + x3)

Combine like terms: 12ix + -3ix = 9ix
fx = (-4 + 9ix + -9ix + -3ix2 + 3ix2 + 36i2 + -9i2x + -4x + -3x + -3x2 + 1x2 + x3)

Combine like terms: 9ix + -9ix = 0
fx = (-4 + 0 + -3ix2 + 3ix2 + 36i2 + -9i2x + -4x + -3x + -3x2 + 1x2 + x3)
fx = (-4 + -3ix2 + 3ix2 + 36i2 + -9i2x + -4x + -3x + -3x2 + 1x2 + x3)

Combine like terms: -3ix2 + 3ix2 = 0
fx = (-4 + 0 + 36i2 + -9i2x + -4x + -3x + -3x2 + 1x2 + x3)
fx = (-4 + 36i2 + -9i2x + -4x + -3x + -3x2 + 1x2 + x3)

Combine like terms: -4x + -3x = -7x
fx = (-4 + 36i2 + -9i2x + -7x + -3x2 + 1x2 + x3)

Combine like terms: -3x2 + 1x2 = -2x2
fx = (-4 + 36i2 + -9i2x + -7x + -2x2 + x3)

Solving
fx = -4 + 36i2 + -9i2x + -7x + -2x2 + x3

Solving for variable 'f'.

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

Divide each side by 'x'.
f = -4x-1 + 36i2x-1 + -9i2 + -7 + -2x + x2

Simplifying
f = -4x-1 + 36i2x-1 + -9i2 + -7 + -2x + x2

Reorder the terms:
f = -7 + -9i2 + 36i2x-1 + -4x-1 + -2x + x2

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