f(x)=(x-4)(x-2)(x-3-2i)(x-3+2i)

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Solution for f(x)=(x-4)(x-2)(x-3-2i)(x-3+2i) equation:

Simplifying
f(x) = (x + -4)(x + -2)(x + -3 + -2i)(x + -3 + 2i)

Multiply f * x
fx = (x + -4)(x + -2)(x + -3 + -2i)(x + -3 + 2i)

Reorder the terms:
fx = (-4 + x)(x + -2)(x + -3 + -2i)(x + -3 + 2i)

Reorder the terms:
fx = (-4 + x)(-2 + x)(x + -3 + -2i)(x + -3 + 2i)

Reorder the terms:
fx = (-4 + x)(-2 + x)(-3 + -2i + x)(x + -3 + 2i)

Reorder the terms:
fx = (-4 + x)(-2 + x)(-3 + -2i + x)(-3 + 2i + x)

Multiply (-4 + x) * (-2 + x)
fx = (-4(-2 + x) + x(-2 + x))(-3 + -2i + x)(-3 + 2i + x)
fx = ((-2 * -4 + x * -4) + x(-2 + x))(-3 + -2i + x)(-3 + 2i + x)
fx = ((8 + -4x) + x(-2 + x))(-3 + -2i + x)(-3 + 2i + x)
fx = (8 + -4x + (-2 * x + x * x))(-3 + -2i + x)(-3 + 2i + x)
fx = (8 + -4x + (-2x + x²))(-3 + -2i + x)(-3 + 2i + x)

Combine like terms: -4x + -2x = -6x
fx = (8 + -6x + x²)(-3 + -2i + x)(-3 + 2i + x)

Multiply (8 + -6x + x²) * (-3 + -2i + x)
fx = (8(-3 + -2i + x) + -6x * (-3 + -2i + x) + x²(-3 + -2i + x))(-3 + 2i + x)
fx = ((-3 * 8 + -2i * 8 + x * 8) + -6x * (-3 + -2i + x) + x²(-3 + -2i + x))(-3 + 2i + x)
fx = ((-24 + -16i + 8x) + -6x * (-3 + -2i + x) + x²(-3 + -2i + x))(-3 + 2i + x)
fx = (-24 + -16i + 8x + (-3 * -6x + -2i * -6x + x * -6x) + x²(-3 + -2i + x))(-3 + 2i + x)

Reorder the terms:
fx = (-24 + -16i + 8x + (12ix + 18x + -6x²) + x²(-3 + -2i + x))(-3 + 2i + x)
fx = (-24 + -16i + 8x + (12ix + 18x + -6x²) + x²(-3 + -2i + x))(-3 + 2i + x)
fx = (-24 + -16i + 8x + 12ix + 18x + -6x² + (-3 * x² + -2i * x² + x * x²))(-3 + 2i + x)

Reorder the terms:
fx = (-24 + -16i + 8x + 12ix + 18x + -6x² + (-2ix² + -3x² + x³))(-3 + 2i + x)
fx = (-24 + -16i + 8x + 12ix + 18x + -6x² + (-2ix² + -3x² + x³))(-3 + 2i + x)

Reorder the terms:
fx = (-24 + -16i + 12ix + -2ix² + 8x + 18x + -6x² + -3x² + x³)(-3 + 2i + x)

Combine like terms: 8x + 18x = 26x
fx = (-24 + -16i + 12ix + -2ix² + 26x + -6x² + -3x² + x³)(-3 + 2i + x)

Combine like terms: -6x² + -3x² = -9x²
fx = (-24 + -16i + 12ix + -2ix² + 26x + -9x² + x³)(-3 + 2i + x)

Multiply (-24 + -16i + 12ix + -2ix² + 26x + -9x² + x³) * (-3 + 2i + x)
fx = (-24(-3 + 2i + x) + -16i * (-3 + 2i + x) + 12ix * (-3 + 2i + x) + -2ix² * (-3 + 2i + x) + 26x * (-3 + 2i + x) + -9x² * (-3 + 2i + x) + x³(-3 + 2i + x))
fx = ((-3 * -24 + 2i * -24 + x * -24) + -16i * (-3 + 2i + x) + 12ix * (-3 + 2i + x) + -2ix² * (-3 + 2i + x) + 26x * (-3 + 2i + x) + -9x² * (-3 + 2i + x) + x³(-3 + 2i + x))
fx = ((72 + -48i + -24x) + -16i * (-3 + 2i + x) + 12ix * (-3 + 2i + x) + -2ix² * (-3 + 2i + x) + 26x * (-3 + 2i + x) + -9x² * (-3 + 2i + x) + x³(-3 + 2i + x))
fx = (72 + -48i + -24x + (-3 * -16i + 2i * -16i + x * -16i) + 12ix * (-3 + 2i + x) + -2ix² * (-3 + 2i + x) + 26x * (-3 + 2i + x) + -9x² * (-3 + 2i + x) + x³(-3 + 2i + x))

Reorder the terms:
fx = (72 + -48i + -24x + (48i + -16ix + -32i²) + 12ix * (-3 + 2i + x) + -2ix² * (-3 + 2i + x) + 26x * (-3 + 2i + x) + -9x² * (-3 + 2i + x) + x³(-3 + 2i + x))
fx = (72 + -48i + -24x + (48i + -16ix + -32i²) + 12ix * (-3 + 2i + x) + -2ix² * (-3 + 2i + x) + 26x * (-3 + 2i + x) + -9x² * (-3 + 2i + x) + x³(-3 + 2i + x))
fx = (72 + -48i + -24x + 48i + -16ix + -32i² + (-3 * 12ix + 2i * 12ix + x * 12ix) + -2ix² * (-3 + 2i + x) + 26x * (-3 + 2i + x) + -9x² * (-3 + 2i + x) + x³(-3 + 2i + x))

Reorder the terms:
fx = (72 + -48i + -24x + 48i + -16ix + -32i² + (-36ix + 12ix² + 24i²x) + -2ix² * (-3 + 2i + x) + 26x * (-3 + 2i + x) + -9x² * (-3 + 2i + x) + x³(-3 + 2i + x))
fx = (72 + -48i + -24x + 48i + -16ix + -32i² + (-36ix + 12ix² + 24i²x) + -2ix² * (-3 + 2i + x) + 26x * (-3 + 2i + x) + -9x² * (-3 + 2i + x) + x³(-3 + 2i + x))
fx = (72 + -48i + -24x + 48i + -16ix + -32i² + -36ix + 12ix² + 24i²x + (-3 * -2ix² + 2i * -2ix² + x * -2ix²) + 26x * (-3 + 2i + x) + -9x² * (-3 + 2i + x) + x³(-3 + 2i + x))

Reorder the terms:
fx = (72 + -48i + -24x + 48i + -16ix + -32i² + -36ix + 12ix² + 24i²x + (6ix² + -2ix³ + -4i²x²) + 26x * (-3 + 2i + x) + -9x² * (-3 + 2i + x) + x³(-3 + 2i + x))
fx = (72 + -48i + -24x + 48i + -16ix + -32i² + -36ix + 12ix² + 24i²x + (6ix² + -2ix³ + -4i²x²) + 26x * (-3 + 2i + x) + -9x² * (-3 + 2i + x) + x³(-3 + 2i + x))
fx = (72 + -48i + -24x + 48i + -16ix + -32i² + -36ix + 12ix² + 24i²x + 6ix² + -2ix³ + -4i²x² + (-3 * 26x + 2i * 26x + x * 26x) + -9x² * (-3 + 2i + x) + x³(-3 + 2i + x))

Reorder the terms:
fx = (72 + -48i + -24x + 48i + -16ix + -32i² + -36ix + 12ix² + 24i²x + 6ix² + -2ix³ + -4i²x² + (52ix + -78x + 26x²) + -9x² * (-3 + 2i + x) + x³(-3 + 2i + x))
fx = (72 + -48i + -24x + 48i + -16ix + -32i² + -36ix + 12ix² + 24i²x + 6ix² + -2ix³ + -4i²x² + (52ix + -78x + 26x²) + -9x² * (-3 + 2i + x) + x³(-3 + 2i + x))
fx = (72 + -48i + -24x + 48i + -16ix + -32i² + -36ix + 12ix² + 24i²x + 6ix² + -2ix³ + -4i²x² + 52ix + -78x + 26x² + (-3 * -9x² + 2i * -9x² + x * -9x²) + x³(-3 + 2i + x))

Reorder the terms:
fx = (72 + -48i + -24x + 48i + -16ix + -32i² + -36ix + 12ix² + 24i²x + 6ix² + -2ix³ + -4i²x² + 52ix + -78x + 26x² + (-18ix² + 27x² + -9x³) + x³(-3 + 2i + x))
fx = (72 + -48i + -24x + 48i + -16ix + -32i² + -36ix + 12ix² + 24i²x + 6ix² + -2ix³ + -4i²x² + 52ix + -78x + 26x² + (-18ix² + 27x² + -9x³) + x³(-3 + 2i + x))
fx = (72 + -48i + -24x + 48i + -16ix + -32i² + -36ix + 12ix² + 24i²x + 6ix² + -2ix³ + -4i²x² + 52ix + -78x + 26x² + -18ix² + 27x² + -9x³ + (-3 * x³ + 2i * x³ + x * x³))

Reorder the terms:
fx = (72 + -48i + -24x + 48i + -16ix + -32i² + -36ix + 12ix² + 24i²x + 6ix² + -2ix³ + -4i²x² + 52ix + -78x + 26x² + -18ix² + 27x² + -9x³ + (2ix³ + -3x³ + x⁴))
fx = (72 + -48i + -24x + 48i + -16ix + -32i² + -36ix + 12ix² + 24i²x + 6ix² + -2ix³ + -4i²x² + 52ix + -78x + 26x² + -18ix² + 27x² + -9x³ + (2ix³ + -3x³ + x⁴))

Reorder the terms:
fx = (72 + -48i + 48i + -16ix + -36ix + 52ix + 12ix² + 6ix² + -18ix² + -2ix³ + 2ix³ + -32i² + 24i²x + -4i²x² + -24x + -78x + 26x² + 27x² + -9x³ + -3x³ + x⁴)

Combine like terms: -48i + 48i = 0
fx = (72 + 0 + -16ix + -36ix + 52ix + 12ix² + 6ix² + -18ix² + -2ix³ + 2ix³ + -32i² + 24i²x + -4i²x² + -24x + -78x + 26x² + 27x² + -9x³ + -3x³ + x⁴)
fx = (72 + -16ix + -36ix + 52ix + 12ix² + 6ix² + -18ix² + -2ix³ + 2ix³ + -32i² + 24i²x + -4i²x² + -24x + -78x + 26x² + 27x² + -9x³ + -3x³ + x⁴)

Combine like terms: -16ix + -36ix = -52ix
fx = (72 + -52ix + 52ix + 12ix² + 6ix² + -18ix² + -2ix³ + 2ix³ + -32i² + 24i²x + -4i²x² + -24x + -78x + 26x² + 27x² + -9x³ + -3x³ + x⁴)

Combine like terms: -52ix + 52ix = 0
fx = (72 + 0 + 12ix² + 6ix² + -18ix² + -2ix³ + 2ix³ + -32i² + 24i²x + -4i²x² + -24x + -78x + 26x² + 27x² + -9x³ + -3x³ + x⁴)
fx = (72 + 12ix² + 6ix² + -18ix² + -2ix³ + 2ix³ + -32i² + 24i²x + -4i²x² + -24x + -78x + 26x² + 27x² + -9x³ + -3x³ + x⁴)

Combine like terms: 12ix² + 6ix² = 18ix²
fx = (72 + 18ix² + -18ix² + -2ix³ + 2ix³ + -32i² + 24i²x + -4i²x² + -24x + -78x + 26x² + 27x² + -9x³ + -3x³ + x⁴)

Combine like terms: 18ix² + -18ix² = 0
fx = (72 + 0 + -2ix³ + 2ix³ + -32i² + 24i²x + -4i²x² + -24x + -78x + 26x² + 27x² + -9x³ + -3x³ + x⁴)
fx = (72 + -2ix³ + 2ix³ + -32i² + 24i²x + -4i²x² + -24x + -78x + 26x² + 27x² + -9x³ + -3x³ + x⁴)

Combine like terms: -2ix³ + 2ix³ = 0
fx = (72 + 0 + -32i² + 24i²x + -4i²x² + -24x + -78x + 26x² + 27x² + -9x³ + -3x³ + x⁴)
fx = (72 + -32i² + 24i²x + -4i²x² + -24x + -78x + 26x² + 27x² + -9x³ + -3x³ + x⁴)

Combine like terms: -24x + -78x = -102x
fx = (72 + -32i² + 24i²x + -4i²x² + -102x + 26x² + 27x² + -9x³ + -3x³ + x⁴)

Combine like terms: 26x² + 27x² = 53x²
fx = (72 + -32i² + 24i²x + -4i²x² + -102x + 53x² + -9x³ + -3x³ + x⁴)

Combine like terms: -9x³ + -3x³ = -12x³
fx = (72 + -32i² + 24i²x + -4i²x² + -102x + 53x² + -12x³ + x⁴)

Solving
fx = 72 + -32i² + 24i²x + -4i²x² + -102x + 53x² + -12x³ + 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 = 72x^-1 + -32i²x^-1 + 24i² + -4i²x + -102 + 53x + -12x² + x³

Simplifying
f = 72x^-1 + -32i²x^-1 + 24i² + -4i²x + -102 + 53x + -12x² + x³

Reorder the terms:
f = -102 + 24i² + -32i²x^-1 + -4i²x + 72x^-1 + 53x + -12x² + x³

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f(x)=(x-4)(x-2)(x-3-2i)(x-3+2i)

Simple and best practice solution for f(x)=(x-4)(x-2)(x-3-2i)(x-3+2i) equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

Solution for f(x)=(x-4)(x-2)(x-3-2i)(x-3+2i) equation:

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