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

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

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

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

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

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

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

Combine like terms: 1x + -1x = 0
fx = x(-1 + 0 + x2)
fx = x(-1 + x2)
fx = (-1 * x + x2 * x)
fx = (-1x + x3)

Solving
fx = -1x + 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 = -1 + x2

Simplifying
f = -1 + x2