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

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


Simplifying
f(x) = 5(x2 + 1)(x2 + -2x + 1)

Multiply f * x
fx = 5(x2 + 1)(x2 + -2x + 1)

Reorder the terms:
fx = 5(1 + x2)(x2 + -2x + 1)

Reorder the terms:
fx = 5(1 + x2)(1 + -2x + x2)

Multiply (1 + x2) * (1 + -2x + x2)
fx = 5(1(1 + -2x + x2) + x2(1 + -2x + x2))
fx = 5((1 * 1 + -2x * 1 + x2 * 1) + x2(1 + -2x + x2))
fx = 5((1 + -2x + 1x2) + x2(1 + -2x + x2))
fx = 5(1 + -2x + 1x2 + (1 * x2 + -2x * x2 + x2 * x2))
fx = 5(1 + -2x + 1x2 + (1x2 + -2x3 + x4))

Combine like terms: 1x2 + 1x2 = 2x2
fx = 5(1 + -2x + 2x2 + -2x3 + x4)
fx = (1 * 5 + -2x * 5 + 2x2 * 5 + -2x3 * 5 + x4 * 5)
fx = (5 + -10x + 10x2 + -10x3 + 5x4)

Solving
fx = 5 + -10x + 10x2 + -10x3 + 5x4

Solving for variable 'f'.

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

Divide each side by 'x'.
f = 5x-1 + -10 + 10x + -10x2 + 5x3

Simplifying
f = 5x-1 + -10 + 10x + -10x2 + 5x3

Reorder the terms:
f = -10 + 5x-1 + 10x + -10x2 + 5x3

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