f(x)=(x^2-5x+6)(x-1)(x+3)

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Solution for f(x)=(x^2-5x+6)(x-1)(x+3) equation: 


Simplifying
f(x) = (x2 + -5x + 6)(x + -1)(x + 3)

Multiply f * x
fx = (x2 + -5x + 6)(x + -1)(x + 3)

Reorder the terms:
fx = (6 + -5x + x2)(x + -1)(x + 3)

Reorder the terms:
fx = (6 + -5x + x2)(-1 + x)(x + 3)

Reorder the terms:
fx = (6 + -5x + x2)(-1 + x)(3 + x)

Multiply (6 + -5x + x2) * (-1 + x)
fx = (6(-1 + x) + -5x * (-1 + x) + x2(-1 + x))(3 + x)
fx = ((-1 * 6 + x * 6) + -5x * (-1 + x) + x2(-1 + x))(3 + x)
fx = ((-6 + 6x) + -5x * (-1 + x) + x2(-1 + x))(3 + x)
fx = (-6 + 6x + (-1 * -5x + x * -5x) + x2(-1 + x))(3 + x)
fx = (-6 + 6x + (5x + -5x2) + x2(-1 + x))(3 + x)
fx = (-6 + 6x + 5x + -5x2 + (-1 * x2 + x * x2))(3 + x)
fx = (-6 + 6x + 5x + -5x2 + (-1x2 + x3))(3 + x)

Combine like terms: 6x + 5x = 11x
fx = (-6 + 11x + -5x2 + -1x2 + x3)(3 + x)

Combine like terms: -5x2 + -1x2 = -6x2
fx = (-6 + 11x + -6x2 + x3)(3 + x)

Multiply (-6 + 11x + -6x2 + x3) * (3 + x)
fx = (-6(3 + x) + 11x * (3 + x) + -6x2 * (3 + x) + x3(3 + x))
fx = ((3 * -6 + x * -6) + 11x * (3 + x) + -6x2 * (3 + x) + x3(3 + x))
fx = ((-18 + -6x) + 11x * (3 + x) + -6x2 * (3 + x) + x3(3 + x))
fx = (-18 + -6x + (3 * 11x + x * 11x) + -6x2 * (3 + x) + x3(3 + x))
fx = (-18 + -6x + (33x + 11x2) + -6x2 * (3 + x) + x3(3 + x))
fx = (-18 + -6x + 33x + 11x2 + (3 * -6x2 + x * -6x2) + x3(3 + x))
fx = (-18 + -6x + 33x + 11x2 + (-18x2 + -6x3) + x3(3 + x))
fx = (-18 + -6x + 33x + 11x2 + -18x2 + -6x3 + (3 * x3 + x * x3))
fx = (-18 + -6x + 33x + 11x2 + -18x2 + -6x3 + (3x3 + x4))

Combine like terms: -6x + 33x = 27x
fx = (-18 + 27x + 11x2 + -18x2 + -6x3 + 3x3 + x4)

Combine like terms: 11x2 + -18x2 = -7x2
fx = (-18 + 27x + -7x2 + -6x3 + 3x3 + x4)

Combine like terms: -6x3 + 3x3 = -3x3
fx = (-18 + 27x + -7x2 + -3x3 + x4)

Solving
fx = -18 + 27x + -7x2 + -3x3 + 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 = -18x-1 + 27 + -7x + -3x2 + x3

Simplifying
f = -18x-1 + 27 + -7x + -3x2 + x3

Reorder the terms:
f = 27 + -18x-1 + -7x + -3x2 + x3

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