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

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


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

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

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

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

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

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

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

Multiply (-3 + 6x + -1x2 + 2x3) * (-5 + 2x2)
fx = (-3(-5 + 2x2) + 6x * (-5 + 2x2) + -1x2 * (-5 + 2x2) + 2x3 * (-5 + 2x2))
fx = ((-5 * -3 + 2x2 * -3) + 6x * (-5 + 2x2) + -1x2 * (-5 + 2x2) + 2x3 * (-5 + 2x2))
fx = ((15 + -6x2) + 6x * (-5 + 2x2) + -1x2 * (-5 + 2x2) + 2x3 * (-5 + 2x2))
fx = (15 + -6x2 + (-5 * 6x + 2x2 * 6x) + -1x2 * (-5 + 2x2) + 2x3 * (-5 + 2x2))
fx = (15 + -6x2 + (-30x + 12x3) + -1x2 * (-5 + 2x2) + 2x3 * (-5 + 2x2))
fx = (15 + -6x2 + -30x + 12x3 + (-5 * -1x2 + 2x2 * -1x2) + 2x3 * (-5 + 2x2))
fx = (15 + -6x2 + -30x + 12x3 + (5x2 + -2x4) + 2x3 * (-5 + 2x2))
fx = (15 + -6x2 + -30x + 12x3 + 5x2 + -2x4 + (-5 * 2x3 + 2x2 * 2x3))
fx = (15 + -6x2 + -30x + 12x3 + 5x2 + -2x4 + (-10x3 + 4x5))

Reorder the terms:
fx = (15 + -30x + -6x2 + 5x2 + 12x3 + -10x3 + -2x4 + 4x5)

Combine like terms: -6x2 + 5x2 = -1x2
fx = (15 + -30x + -1x2 + 12x3 + -10x3 + -2x4 + 4x5)

Combine like terms: 12x3 + -10x3 = 2x3
fx = (15 + -30x + -1x2 + 2x3 + -2x4 + 4x5)

Solving
fx = 15 + -30x + -1x2 + 2x3 + -2x4 + 4x5

Solving for variable 'f'.

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

Divide each side by 'x'.
f = 15x-1 + -30 + -1x + 2x2 + -2x3 + 4x4

Simplifying
f = 15x-1 + -30 + -1x + 2x2 + -2x3 + 4x4

Reorder the terms:
f = -30 + 15x-1 + -1x + 2x2 + -2x3 + 4x4

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