f(x)=(x-5)(x-2+3i)(x-2-3i)

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Solution for f(x)=(x-5)(x-2+3i)(x-2-3i) equation: 


Simplifying
f(x) = (x + -5)(x + -2 + 3i)(x + -2 + -3i)

Multiply f * x
fx = (x + -5)(x + -2 + 3i)(x + -2 + -3i)

Reorder the terms:
fx = (-5 + x)(x + -2 + 3i)(x + -2 + -3i)

Reorder the terms:
fx = (-5 + x)(-2 + 3i + x)(x + -2 + -3i)

Reorder the terms:
fx = (-5 + x)(-2 + 3i + x)(-2 + -3i + x)

Multiply (-5 + x) * (-2 + 3i + x)
fx = (-5(-2 + 3i + x) + x(-2 + 3i + x))(-2 + -3i + x)
fx = ((-2 * -5 + 3i * -5 + x * -5) + x(-2 + 3i + x))(-2 + -3i + x)
fx = ((10 + -15i + -5x) + x(-2 + 3i + x))(-2 + -3i + x)
fx = (10 + -15i + -5x + (-2 * x + 3i * x + x * x))(-2 + -3i + x)

Reorder the terms:
fx = (10 + -15i + -5x + (3ix + -2x + x2))(-2 + -3i + x)
fx = (10 + -15i + -5x + (3ix + -2x + x2))(-2 + -3i + x)

Reorder the terms:
fx = (10 + -15i + 3ix + -5x + -2x + x2)(-2 + -3i + x)

Combine like terms: -5x + -2x = -7x
fx = (10 + -15i + 3ix + -7x + x2)(-2 + -3i + x)

Multiply (10 + -15i + 3ix + -7x + x2) * (-2 + -3i + x)
fx = (10(-2 + -3i + x) + -15i * (-2 + -3i + x) + 3ix * (-2 + -3i + x) + -7x * (-2 + -3i + x) + x2(-2 + -3i + x))
fx = ((-2 * 10 + -3i * 10 + x * 10) + -15i * (-2 + -3i + x) + 3ix * (-2 + -3i + x) + -7x * (-2 + -3i + x) + x2(-2 + -3i + x))
fx = ((-20 + -30i + 10x) + -15i * (-2 + -3i + x) + 3ix * (-2 + -3i + x) + -7x * (-2 + -3i + x) + x2(-2 + -3i + x))
fx = (-20 + -30i + 10x + (-2 * -15i + -3i * -15i + x * -15i) + 3ix * (-2 + -3i + x) + -7x * (-2 + -3i + x) + x2(-2 + -3i + x))

Reorder the terms:
fx = (-20 + -30i + 10x + (30i + -15ix + 45i2) + 3ix * (-2 + -3i + x) + -7x * (-2 + -3i + x) + x2(-2 + -3i + x))
fx = (-20 + -30i + 10x + (30i + -15ix + 45i2) + 3ix * (-2 + -3i + x) + -7x * (-2 + -3i + x) + x2(-2 + -3i + x))
fx = (-20 + -30i + 10x + 30i + -15ix + 45i2 + (-2 * 3ix + -3i * 3ix + x * 3ix) + -7x * (-2 + -3i + x) + x2(-2 + -3i + x))

Reorder the terms:
fx = (-20 + -30i + 10x + 30i + -15ix + 45i2 + (-6ix + 3ix2 + -9i2x) + -7x * (-2 + -3i + x) + x2(-2 + -3i + x))
fx = (-20 + -30i + 10x + 30i + -15ix + 45i2 + (-6ix + 3ix2 + -9i2x) + -7x * (-2 + -3i + x) + x2(-2 + -3i + x))
fx = (-20 + -30i + 10x + 30i + -15ix + 45i2 + -6ix + 3ix2 + -9i2x + (-2 * -7x + -3i * -7x + x * -7x) + x2(-2 + -3i + x))

Reorder the terms:
fx = (-20 + -30i + 10x + 30i + -15ix + 45i2 + -6ix + 3ix2 + -9i2x + (21ix + 14x + -7x2) + x2(-2 + -3i + x))
fx = (-20 + -30i + 10x + 30i + -15ix + 45i2 + -6ix + 3ix2 + -9i2x + (21ix + 14x + -7x2) + x2(-2 + -3i + x))
fx = (-20 + -30i + 10x + 30i + -15ix + 45i2 + -6ix + 3ix2 + -9i2x + 21ix + 14x + -7x2 + (-2 * x2 + -3i * x2 + x * x2))

Reorder the terms:
fx = (-20 + -30i + 10x + 30i + -15ix + 45i2 + -6ix + 3ix2 + -9i2x + 21ix + 14x + -7x2 + (-3ix2 + -2x2 + x3))
fx = (-20 + -30i + 10x + 30i + -15ix + 45i2 + -6ix + 3ix2 + -9i2x + 21ix + 14x + -7x2 + (-3ix2 + -2x2 + x3))

Reorder the terms:
fx = (-20 + -30i + 30i + -15ix + -6ix + 21ix + 3ix2 + -3ix2 + 45i2 + -9i2x + 10x + 14x + -7x2 + -2x2 + x3)

Combine like terms: -30i + 30i = 0
fx = (-20 + 0 + -15ix + -6ix + 21ix + 3ix2 + -3ix2 + 45i2 + -9i2x + 10x + 14x + -7x2 + -2x2 + x3)
fx = (-20 + -15ix + -6ix + 21ix + 3ix2 + -3ix2 + 45i2 + -9i2x + 10x + 14x + -7x2 + -2x2 + x3)

Combine like terms: -15ix + -6ix = -21ix
fx = (-20 + -21ix + 21ix + 3ix2 + -3ix2 + 45i2 + -9i2x + 10x + 14x + -7x2 + -2x2 + x3)

Combine like terms: -21ix + 21ix = 0
fx = (-20 + 0 + 3ix2 + -3ix2 + 45i2 + -9i2x + 10x + 14x + -7x2 + -2x2 + x3)
fx = (-20 + 3ix2 + -3ix2 + 45i2 + -9i2x + 10x + 14x + -7x2 + -2x2 + x3)

Combine like terms: 3ix2 + -3ix2 = 0
fx = (-20 + 0 + 45i2 + -9i2x + 10x + 14x + -7x2 + -2x2 + x3)
fx = (-20 + 45i2 + -9i2x + 10x + 14x + -7x2 + -2x2 + x3)

Combine like terms: 10x + 14x = 24x
fx = (-20 + 45i2 + -9i2x + 24x + -7x2 + -2x2 + x3)

Combine like terms: -7x2 + -2x2 = -9x2
fx = (-20 + 45i2 + -9i2x + 24x + -9x2 + x3)

Solving
fx = -20 + 45i2 + -9i2x + 24x + -9x2 + 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 = -20x-1 + 45i2x-1 + -9i2 + 24 + -9x + x2

Simplifying
f = -20x-1 + 45i2x-1 + -9i2 + 24 + -9x + x2

Reorder the terms:
f = 24 + -9i2 + 45i2x-1 + -20x-1 + -9x + x2

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