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

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

Simplifying
f(x) = (x + -3)(x + -3)[x + -1(-5 + -2i)][x + -1(-5 + 2i)]

Multiply f * x
fx = (x + -3)(x + -3)[x + -1(-5 + -2i)][x + -1(-5 + 2i)]

Reorder the terms:
fx = (-3 + x)(x + -3)[x + -1(-5 + -2i)][x + -1(-5 + 2i)]

Reorder the terms:
fx = (-3 + x)(-3 + x)[x + -1(-5 + -2i)][x + -1(-5 + 2i)]
fx = (-3 + x)(-3 + x)[x + (-5 * -1 + -2i * -1)][x + -1(-5 + 2i)]
fx = (-3 + x)(-3 + x)[x + (5 + 2i)][x + -1(-5 + 2i)]

Reorder the terms:
fx = (-3 + x)(-3 + x)[5 + 2i + x][x + -1(-5 + 2i)]
fx = (-3 + x)(-3 + x)[5 + 2i + x][x + (-5 * -1 + 2i * -1)]
fx = (-3 + x)(-3 + x)[5 + 2i + x][x + (5 + -2i)]

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

Multiply (-3 + x) * (-3 + x)
fx = (-3(-3 + x) + x(-3 + x))[5 + 2i + x][5 + -2i + x]
fx = ((-3 * -3 + x * -3) + x(-3 + x))[5 + 2i + x][5 + -2i + x]
fx = ((9 + -3x) + x(-3 + x))[5 + 2i + x][5 + -2i + x]
fx = (9 + -3x + (-3 * x + x * x))[5 + 2i + x][5 + -2i + x]
fx = (9 + -3x + (-3x + x²))[5 + 2i + x][5 + -2i + x]

Combine like terms: -3x + -3x = -6x
fx = (9 + -6x + x²)[5 + 2i + x][5 + -2i + x]

Multiply (9 + -6x + x²) * [5 + 2i + x]
fx = (9[5 + 2i + x] + -6x * [5 + 2i + x] + x²[5 + 2i + x])[5 + -2i + x]
fx = ([5 * 9 + 2i * 9 + x * 9] + -6x * [5 + 2i + x] + x²[5 + 2i + x])[5 + -2i + x]
fx = ([45 + 18i + 9x] + -6x * [5 + 2i + x] + x²[5 + 2i + x])[5 + -2i + x]
fx = (45 + 18i + 9x + [5 * -6x + 2i * -6x + x * -6x] + x²[5 + 2i + x])[5 + -2i + x]

Reorder the terms:
fx = (45 + 18i + 9x + [-12ix + -30x + -6x²] + x²[5 + 2i + x])[5 + -2i + x]
fx = (45 + 18i + 9x + [-12ix + -30x + -6x²] + x²[5 + 2i + x])[5 + -2i + x]
fx = (45 + 18i + 9x + -12ix + -30x + -6x² + [5 * x² + 2i * x² + x * x²])[5 + -2i + x]

Reorder the terms:
fx = (45 + 18i + 9x + -12ix + -30x + -6x² + [2ix² + 5x² + x³])[5 + -2i + x]
fx = (45 + 18i + 9x + -12ix + -30x + -6x² + [2ix² + 5x² + x³])[5 + -2i + x]

Reorder the terms:
fx = (45 + 18i + -12ix + 2ix² + 9x + -30x + -6x² + 5x² + x³)[5 + -2i + x]

Combine like terms: 9x + -30x = -21x
fx = (45 + 18i + -12ix + 2ix² + -21x + -6x² + 5x² + x³)[5 + -2i + x]

Combine like terms: -6x² + 5x² = -1x²
fx = (45 + 18i + -12ix + 2ix² + -21x + -1x² + x³)[5 + -2i + x]

Multiply (45 + 18i + -12ix + 2ix² + -21x + -1x² + x³) * [5 + -2i + x]
fx = (45[5 + -2i + x] + 18i * [5 + -2i + x] + -12ix * [5 + -2i + x] + 2ix² * [5 + -2i + x] + -21x * [5 + -2i + x] + -1x² * [5 + -2i + x] + x³[5 + -2i + x])
fx = ([5 * 45 + -2i * 45 + x * 45] + 18i * [5 + -2i + x] + -12ix * [5 + -2i + x] + 2ix² * [5 + -2i + x] + -21x * [5 + -2i + x] + -1x² * [5 + -2i + x] + x³[5 + -2i + x])
fx = ([225 + -90i + 45x] + 18i * [5 + -2i + x] + -12ix * [5 + -2i + x] + 2ix² * [5 + -2i + x] + -21x * [5 + -2i + x] + -1x² * [5 + -2i + x] + x³[5 + -2i + x])
fx = (225 + -90i + 45x + [5 * 18i + -2i * 18i + x * 18i] + -12ix * [5 + -2i + x] + 2ix² * [5 + -2i + x] + -21x * [5 + -2i + x] + -1x² * [5 + -2i + x] + x³[5 + -2i + x])

Reorder the terms:
fx = (225 + -90i + 45x + [90i + 18ix + -36i²] + -12ix * [5 + -2i + x] + 2ix² * [5 + -2i + x] + -21x * [5 + -2i + x] + -1x² * [5 + -2i + x] + x³[5 + -2i + x])
fx = (225 + -90i + 45x + [90i + 18ix + -36i²] + -12ix * [5 + -2i + x] + 2ix² * [5 + -2i + x] + -21x * [5 + -2i + x] + -1x² * [5 + -2i + x] + x³[5 + -2i + x])
fx = (225 + -90i + 45x + 90i + 18ix + -36i² + [5 * -12ix + -2i * -12ix + x * -12ix] + 2ix² * [5 + -2i + x] + -21x * [5 + -2i + x] + -1x² * [5 + -2i + x] + x³[5 + -2i + x])

Reorder the terms:
fx = (225 + -90i + 45x + 90i + 18ix + -36i² + [-60ix + -12ix² + 24i²x] + 2ix² * [5 + -2i + x] + -21x * [5 + -2i + x] + -1x² * [5 + -2i + x] + x³[5 + -2i + x])
fx = (225 + -90i + 45x + 90i + 18ix + -36i² + [-60ix + -12ix² + 24i²x] + 2ix² * [5 + -2i + x] + -21x * [5 + -2i + x] + -1x² * [5 + -2i + x] + x³[5 + -2i + x])
fx = (225 + -90i + 45x + 90i + 18ix + -36i² + -60ix + -12ix² + 24i²x + [5 * 2ix² + -2i * 2ix² + x * 2ix²] + -21x * [5 + -2i + x] + -1x² * [5 + -2i + x] + x³[5 + -2i + x])

Reorder the terms:
fx = (225 + -90i + 45x + 90i + 18ix + -36i² + -60ix + -12ix² + 24i²x + [10ix² + 2ix³ + -4i²x²] + -21x * [5 + -2i + x] + -1x² * [5 + -2i + x] + x³[5 + -2i + x])
fx = (225 + -90i + 45x + 90i + 18ix + -36i² + -60ix + -12ix² + 24i²x + [10ix² + 2ix³ + -4i²x²] + -21x * [5 + -2i + x] + -1x² * [5 + -2i + x] + x³[5 + -2i + x])
fx = (225 + -90i + 45x + 90i + 18ix + -36i² + -60ix + -12ix² + 24i²x + 10ix² + 2ix³ + -4i²x² + [5 * -21x + -2i * -21x + x * -21x] + -1x² * [5 + -2i + x] + x³[5 + -2i + x])

Reorder the terms:
fx = (225 + -90i + 45x + 90i + 18ix + -36i² + -60ix + -12ix² + 24i²x + 10ix² + 2ix³ + -4i²x² + [42ix + -105x + -21x²] + -1x² * [5 + -2i + x] + x³[5 + -2i + x])
fx = (225 + -90i + 45x + 90i + 18ix + -36i² + -60ix + -12ix² + 24i²x + 10ix² + 2ix³ + -4i²x² + [42ix + -105x + -21x²] + -1x² * [5 + -2i + x] + x³[5 + -2i + x])
fx = (225 + -90i + 45x + 90i + 18ix + -36i² + -60ix + -12ix² + 24i²x + 10ix² + 2ix³ + -4i²x² + 42ix + -105x + -21x² + [5 * -1x² + -2i * -1x² + x * -1x²] + x³[5 + -2i + x])

Reorder the terms:
fx = (225 + -90i + 45x + 90i + 18ix + -36i² + -60ix + -12ix² + 24i²x + 10ix² + 2ix³ + -4i²x² + 42ix + -105x + -21x² + [2ix² + -5x² + -1x³] + x³[5 + -2i + x])
fx = (225 + -90i + 45x + 90i + 18ix + -36i² + -60ix + -12ix² + 24i²x + 10ix² + 2ix³ + -4i²x² + 42ix + -105x + -21x² + [2ix² + -5x² + -1x³] + x³[5 + -2i + x])
fx = (225 + -90i + 45x + 90i + 18ix + -36i² + -60ix + -12ix² + 24i²x + 10ix² + 2ix³ + -4i²x² + 42ix + -105x + -21x² + 2ix² + -5x² + -1x³ + [5 * x³ + -2i * x³ + x * x³])

Reorder the terms:
fx = (225 + -90i + 45x + 90i + 18ix + -36i² + -60ix + -12ix² + 24i²x + 10ix² + 2ix³ + -4i²x² + 42ix + -105x + -21x² + 2ix² + -5x² + -1x³ + [-2ix³ + 5x³ + x⁴])
fx = (225 + -90i + 45x + 90i + 18ix + -36i² + -60ix + -12ix² + 24i²x + 10ix² + 2ix³ + -4i²x² + 42ix + -105x + -21x² + 2ix² + -5x² + -1x³ + [-2ix³ + 5x³ + x⁴])

Reorder the terms:
fx = (225 + -90i + 90i + 18ix + -60ix + 42ix + -12ix² + 10ix² + 2ix² + 2ix³ + -2ix³ + -36i² + 24i²x + -4i²x² + 45x + -105x + -21x² + -5x² + -1x³ + 5x³ + x⁴)

Combine like terms: -90i + 90i = 0
fx = (225 + 0 + 18ix + -60ix + 42ix + -12ix² + 10ix² + 2ix² + 2ix³ + -2ix³ + -36i² + 24i²x + -4i²x² + 45x + -105x + -21x² + -5x² + -1x³ + 5x³ + x⁴)
fx = (225 + 18ix + -60ix + 42ix + -12ix² + 10ix² + 2ix² + 2ix³ + -2ix³ + -36i² + 24i²x + -4i²x² + 45x + -105x + -21x² + -5x² + -1x³ + 5x³ + x⁴)

Combine like terms: 18ix + -60ix = -42ix
fx = (225 + -42ix + 42ix + -12ix² + 10ix² + 2ix² + 2ix³ + -2ix³ + -36i² + 24i²x + -4i²x² + 45x + -105x + -21x² + -5x² + -1x³ + 5x³ + x⁴)

Combine like terms: -42ix + 42ix = 0
fx = (225 + 0 + -12ix² + 10ix² + 2ix² + 2ix³ + -2ix³ + -36i² + 24i²x + -4i²x² + 45x + -105x + -21x² + -5x² + -1x³ + 5x³ + x⁴)
fx = (225 + -12ix² + 10ix² + 2ix² + 2ix³ + -2ix³ + -36i² + 24i²x + -4i²x² + 45x + -105x + -21x² + -5x² + -1x³ + 5x³ + x⁴)

Combine like terms: -12ix² + 10ix² = -2ix²
fx = (225 + -2ix² + 2ix² + 2ix³ + -2ix³ + -36i² + 24i²x + -4i²x² + 45x + -105x + -21x² + -5x² + -1x³ + 5x³ + x⁴)

Combine like terms: -2ix² + 2ix² = 0
fx = (225 + 0 + 2ix³ + -2ix³ + -36i² + 24i²x + -4i²x² + 45x + -105x + -21x² + -5x² + -1x³ + 5x³ + x⁴)
fx = (225 + 2ix³ + -2ix³ + -36i² + 24i²x + -4i²x² + 45x + -105x + -21x² + -5x² + -1x³ + 5x³ + x⁴)

Combine like terms: 2ix³ + -2ix³ = 0
fx = (225 + 0 + -36i² + 24i²x + -4i²x² + 45x + -105x + -21x² + -5x² + -1x³ + 5x³ + x⁴)
fx = (225 + -36i² + 24i²x + -4i²x² + 45x + -105x + -21x² + -5x² + -1x³ + 5x³ + x⁴)

Combine like terms: 45x + -105x = -60x
fx = (225 + -36i² + 24i²x + -4i²x² + -60x + -21x² + -5x² + -1x³ + 5x³ + x⁴)

Combine like terms: -21x² + -5x² = -26x²
fx = (225 + -36i² + 24i²x + -4i²x² + -60x + -26x² + -1x³ + 5x³ + x⁴)

Combine like terms: -1x³ + 5x³ = 4x³
fx = (225 + -36i² + 24i²x + -4i²x² + -60x + -26x² + 4x³ + x⁴)

Solving
fx = 225 + -36i² + 24i²x + -4i²x² + -60x + -26x² + 4x³ + 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 = 225x^-1 + -36i²x^-1 + 24i² + -4i²x + -60 + -26x + 4x² + x³

Simplifying
f = 225x^-1 + -36i²x^-1 + 24i² + -4i²x + -60 + -26x + 4x² + x³

Reorder the terms:
f = -60 + 24i² + -36i²x^-1 + -4i²x + 225x^-1 + -26x + 4x² + x³

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

Simple and best practice solution for f(x)=(x-3)(x-3)[x-(-5-2i)][x-(-5+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-3)(x-3)[x-(-5-2i)][x-(-5+2i)] equation:

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