f(x)=(4x-5)(3x^3-x^2+1)

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Solution for f(x)=(4x-5)(3x^3-x^2+1) equation: 


Simplifying
f(x) = (4x + -5)(3x3 + -1x2 + 1)

Multiply f * x
fx = (4x + -5)(3x3 + -1x2 + 1)

Reorder the terms:
fx = (-5 + 4x)(3x3 + -1x2 + 1)

Reorder the terms:
fx = (-5 + 4x)(1 + -1x2 + 3x3)

Multiply (-5 + 4x) * (1 + -1x2 + 3x3)
fx = (-5(1 + -1x2 + 3x3) + 4x * (1 + -1x2 + 3x3))
fx = ((1 * -5 + -1x2 * -5 + 3x3 * -5) + 4x * (1 + -1x2 + 3x3))
fx = ((-5 + 5x2 + -15x3) + 4x * (1 + -1x2 + 3x3))
fx = (-5 + 5x2 + -15x3 + (1 * 4x + -1x2 * 4x + 3x3 * 4x))
fx = (-5 + 5x2 + -15x3 + (4x + -4x3 + 12x4))

Reorder the terms:
fx = (-5 + 4x + 5x2 + -15x3 + -4x3 + 12x4)

Combine like terms: -15x3 + -4x3 = -19x3
fx = (-5 + 4x + 5x2 + -19x3 + 12x4)

Solving
fx = -5 + 4x + 5x2 + -19x3 + 12x4

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 + 4 + 5x + -19x2 + 12x3

Simplifying
f = -5x-1 + 4 + 5x + -19x2 + 12x3

Reorder the terms:
f = 4 + -5x-1 + 5x + -19x2 + 12x3

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