f(x)=0.25(x+1)(x+2)(x-1)

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Solution for f(x)=0.25(x+1)(x+2)(x-1) equation: 


Simplifying
f(x) = 0.25(x + 1)(x + 2)(x + -1)

Multiply f * x
fx = 0.25(x + 1)(x + 2)(x + -1)

Reorder the terms:
fx = 0.25(1 + x)(x + 2)(x + -1)

Reorder the terms:
fx = 0.25(1 + x)(2 + x)(x + -1)

Reorder the terms:
fx = 0.25(1 + x)(2 + x)(-1 + x)

Multiply (1 + x) * (2 + x)
fx = 0.25(1(2 + x) + x(2 + x))(-1 + x)
fx = 0.25((2 * 1 + x * 1) + x(2 + x))(-1 + x)
fx = 0.25((2 + 1x) + x(2 + x))(-1 + x)
fx = 0.25(2 + 1x + (2 * x + x * x))(-1 + x)
fx = 0.25(2 + 1x + (2x + x2))(-1 + x)

Combine like terms: 1x + 2x = 3x
fx = 0.25(2 + 3x + x2)(-1 + x)

Multiply (2 + 3x + x2) * (-1 + x)
fx = 0.25(2(-1 + x) + 3x * (-1 + x) + x2(-1 + x))
fx = 0.25((-1 * 2 + x * 2) + 3x * (-1 + x) + x2(-1 + x))
fx = 0.25((-2 + 2x) + 3x * (-1 + x) + x2(-1 + x))
fx = 0.25(-2 + 2x + (-1 * 3x + x * 3x) + x2(-1 + x))
fx = 0.25(-2 + 2x + (-3x + 3x2) + x2(-1 + x))
fx = 0.25(-2 + 2x + -3x + 3x2 + (-1 * x2 + x * x2))
fx = 0.25(-2 + 2x + -3x + 3x2 + (-1x2 + x3))

Combine like terms: 2x + -3x = -1x
fx = 0.25(-2 + -1x + 3x2 + -1x2 + x3)

Combine like terms: 3x2 + -1x2 = 2x2
fx = 0.25(-2 + -1x + 2x2 + x3)
fx = (-2 * 0.25 + -1x * 0.25 + 2x2 * 0.25 + x3 * 0.25)
fx = (-0.5 + -0.25x + 0.5x2 + 0.25x3)

Solving
fx = -0.5 + -0.25x + 0.5x2 + 0.25x3

Solving for variable 'f'.

Move all terms containing f to the left, all other terms to the right.

Divide each side by 'x'.
f = -0.5x-1 + -0.25 + 0.5x + 0.25x2

Simplifying
f = -0.5x-1 + -0.25 + 0.5x + 0.25x2

Reorder the terms:
f = -0.25 + -0.5x-1 + 0.5x + 0.25x2

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