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

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


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

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

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

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

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

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

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

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

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

Multiply (-12 + -4i + -1ix + 1x + x2) * (-3 + 1i + x)
fx = (-12(-3 + 1i + x) + -4i * (-3 + 1i + x) + -1ix * (-3 + 1i + x) + 1x * (-3 + 1i + x) + x2(-3 + 1i + x))
fx = ((-3 * -12 + 1i * -12 + x * -12) + -4i * (-3 + 1i + x) + -1ix * (-3 + 1i + x) + 1x * (-3 + 1i + x) + x2(-3 + 1i + x))
fx = ((36 + -12i + -12x) + -4i * (-3 + 1i + x) + -1ix * (-3 + 1i + x) + 1x * (-3 + 1i + x) + x2(-3 + 1i + x))
fx = (36 + -12i + -12x + (-3 * -4i + 1i * -4i + x * -4i) + -1ix * (-3 + 1i + x) + 1x * (-3 + 1i + x) + x2(-3 + 1i + x))

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

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

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

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

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

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

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

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

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

Combine like terms: -12x + -3x = -15x
fx = (36 + -4i2 + -1i2x + -15x + 1x2 + -3x2 + x3)

Combine like terms: 1x2 + -3x2 = -2x2
fx = (36 + -4i2 + -1i2x + -15x + -2x2 + x3)

Solving
fx = 36 + -4i2 + -1i2x + -15x + -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 = 36x-1 + -4i2x-1 + -1i2 + -15 + -2x + x2

Simplifying
f = 36x-1 + -4i2x-1 + -1i2 + -15 + -2x + x2

Reorder the terms:
f = -15 + -1i2 + -4i2x-1 + 36x-1 + -2x + x2

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