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

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


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

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

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

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

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

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

Solving
fx = 1x + 3x2 + 2x3

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 + 3x + 2x2

Simplifying
f = 1 + 3x + 2x2

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