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

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


Simplifying
f(x) = (x2 + 3x + -1)(2x2 + -5x + 1)

Multiply f * x
fx = (x2 + 3x + -1)(2x2 + -5x + 1)

Reorder the terms:
fx = (-1 + 3x + x2)(2x2 + -5x + 1)

Reorder the terms:
fx = (-1 + 3x + x2)(1 + -5x + 2x2)

Multiply (-1 + 3x + x2) * (1 + -5x + 2x2)
fx = (-1(1 + -5x + 2x2) + 3x * (1 + -5x + 2x2) + x2(1 + -5x + 2x2))
fx = ((1 * -1 + -5x * -1 + 2x2 * -1) + 3x * (1 + -5x + 2x2) + x2(1 + -5x + 2x2))
fx = ((-1 + 5x + -2x2) + 3x * (1 + -5x + 2x2) + x2(1 + -5x + 2x2))
fx = (-1 + 5x + -2x2 + (1 * 3x + -5x * 3x + 2x2 * 3x) + x2(1 + -5x + 2x2))
fx = (-1 + 5x + -2x2 + (3x + -15x2 + 6x3) + x2(1 + -5x + 2x2))
fx = (-1 + 5x + -2x2 + 3x + -15x2 + 6x3 + (1 * x2 + -5x * x2 + 2x2 * x2))
fx = (-1 + 5x + -2x2 + 3x + -15x2 + 6x3 + (1x2 + -5x3 + 2x4))

Reorder the terms:
fx = (-1 + 5x + 3x + -2x2 + -15x2 + 1x2 + 6x3 + -5x3 + 2x4)

Combine like terms: 5x + 3x = 8x
fx = (-1 + 8x + -2x2 + -15x2 + 1x2 + 6x3 + -5x3 + 2x4)

Combine like terms: -2x2 + -15x2 = -17x2
fx = (-1 + 8x + -17x2 + 1x2 + 6x3 + -5x3 + 2x4)

Combine like terms: -17x2 + 1x2 = -16x2
fx = (-1 + 8x + -16x2 + 6x3 + -5x3 + 2x4)

Combine like terms: 6x3 + -5x3 = 1x3
fx = (-1 + 8x + -16x2 + 1x3 + 2x4)

Solving
fx = -1 + 8x + -16x2 + 1x3 + 2x4

Solving for variable 'f'.

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

Divide each side by 'x'.
f = -1x-1 + 8 + -16x + x2 + 2x3

Simplifying
f = -1x-1 + 8 + -16x + x2 + 2x3

Reorder the terms:
f = 8 + -1x-1 + -16x + x2 + 2x3

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