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

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


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

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

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

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

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

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

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

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

Multiply (1 + -2x + -1x2 + 2x3) * (3 + x2)
fx = (1(3 + x2) + -2x * (3 + x2) + -1x2 * (3 + x2) + 2x3 * (3 + x2))(-5 + 2x2)
fx = ((3 * 1 + x2 * 1) + -2x * (3 + x2) + -1x2 * (3 + x2) + 2x3 * (3 + x2))(-5 + 2x2)
fx = ((3 + 1x2) + -2x * (3 + x2) + -1x2 * (3 + x2) + 2x3 * (3 + x2))(-5 + 2x2)
fx = (3 + 1x2 + (3 * -2x + x2 * -2x) + -1x2 * (3 + x2) + 2x3 * (3 + x2))(-5 + 2x2)
fx = (3 + 1x2 + (-6x + -2x3) + -1x2 * (3 + x2) + 2x3 * (3 + x2))(-5 + 2x2)
fx = (3 + 1x2 + -6x + -2x3 + (3 * -1x2 + x2 * -1x2) + 2x3 * (3 + x2))(-5 + 2x2)
fx = (3 + 1x2 + -6x + -2x3 + (-3x2 + -1x4) + 2x3 * (3 + x2))(-5 + 2x2)
fx = (3 + 1x2 + -6x + -2x3 + -3x2 + -1x4 + (3 * 2x3 + x2 * 2x3))(-5 + 2x2)
fx = (3 + 1x2 + -6x + -2x3 + -3x2 + -1x4 + (6x3 + 2x5))(-5 + 2x2)

Reorder the terms:
fx = (3 + -6x + 1x2 + -3x2 + -2x3 + 6x3 + -1x4 + 2x5)(-5 + 2x2)

Combine like terms: 1x2 + -3x2 = -2x2
fx = (3 + -6x + -2x2 + -2x3 + 6x3 + -1x4 + 2x5)(-5 + 2x2)

Combine like terms: -2x3 + 6x3 = 4x3
fx = (3 + -6x + -2x2 + 4x3 + -1x4 + 2x5)(-5 + 2x2)

Multiply (3 + -6x + -2x2 + 4x3 + -1x4 + 2x5) * (-5 + 2x2)
fx = (3(-5 + 2x2) + -6x * (-5 + 2x2) + -2x2 * (-5 + 2x2) + 4x3 * (-5 + 2x2) + -1x4 * (-5 + 2x2) + 2x5 * (-5 + 2x2))
fx = ((-5 * 3 + 2x2 * 3) + -6x * (-5 + 2x2) + -2x2 * (-5 + 2x2) + 4x3 * (-5 + 2x2) + -1x4 * (-5 + 2x2) + 2x5 * (-5 + 2x2))
fx = ((-15 + 6x2) + -6x * (-5 + 2x2) + -2x2 * (-5 + 2x2) + 4x3 * (-5 + 2x2) + -1x4 * (-5 + 2x2) + 2x5 * (-5 + 2x2))
fx = (-15 + 6x2 + (-5 * -6x + 2x2 * -6x) + -2x2 * (-5 + 2x2) + 4x3 * (-5 + 2x2) + -1x4 * (-5 + 2x2) + 2x5 * (-5 + 2x2))
fx = (-15 + 6x2 + (30x + -12x3) + -2x2 * (-5 + 2x2) + 4x3 * (-5 + 2x2) + -1x4 * (-5 + 2x2) + 2x5 * (-5 + 2x2))
fx = (-15 + 6x2 + 30x + -12x3 + (-5 * -2x2 + 2x2 * -2x2) + 4x3 * (-5 + 2x2) + -1x4 * (-5 + 2x2) + 2x5 * (-5 + 2x2))
fx = (-15 + 6x2 + 30x + -12x3 + (10x2 + -4x4) + 4x3 * (-5 + 2x2) + -1x4 * (-5 + 2x2) + 2x5 * (-5 + 2x2))
fx = (-15 + 6x2 + 30x + -12x3 + 10x2 + -4x4 + (-5 * 4x3 + 2x2 * 4x3) + -1x4 * (-5 + 2x2) + 2x5 * (-5 + 2x2))
fx = (-15 + 6x2 + 30x + -12x3 + 10x2 + -4x4 + (-20x3 + 8x5) + -1x4 * (-5 + 2x2) + 2x5 * (-5 + 2x2))
fx = (-15 + 6x2 + 30x + -12x3 + 10x2 + -4x4 + -20x3 + 8x5 + (-5 * -1x4 + 2x2 * -1x4) + 2x5 * (-5 + 2x2))
fx = (-15 + 6x2 + 30x + -12x3 + 10x2 + -4x4 + -20x3 + 8x5 + (5x4 + -2x6) + 2x5 * (-5 + 2x2))
fx = (-15 + 6x2 + 30x + -12x3 + 10x2 + -4x4 + -20x3 + 8x5 + 5x4 + -2x6 + (-5 * 2x5 + 2x2 * 2x5))
fx = (-15 + 6x2 + 30x + -12x3 + 10x2 + -4x4 + -20x3 + 8x5 + 5x4 + -2x6 + (-10x5 + 4x7))

Reorder the terms:
fx = (-15 + 30x + 6x2 + 10x2 + -12x3 + -20x3 + -4x4 + 5x4 + 8x5 + -10x5 + -2x6 + 4x7)

Combine like terms: 6x2 + 10x2 = 16x2
fx = (-15 + 30x + 16x2 + -12x3 + -20x3 + -4x4 + 5x4 + 8x5 + -10x5 + -2x6 + 4x7)

Combine like terms: -12x3 + -20x3 = -32x3
fx = (-15 + 30x + 16x2 + -32x3 + -4x4 + 5x4 + 8x5 + -10x5 + -2x6 + 4x7)

Combine like terms: -4x4 + 5x4 = 1x4
fx = (-15 + 30x + 16x2 + -32x3 + 1x4 + 8x5 + -10x5 + -2x6 + 4x7)

Combine like terms: 8x5 + -10x5 = -2x5
fx = (-15 + 30x + 16x2 + -32x3 + 1x4 + -2x5 + -2x6 + 4x7)

Solving
fx = -15 + 30x + 16x2 + -32x3 + 1x4 + -2x5 + -2x6 + 4x7

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 + 16x + -32x2 + x3 + -2x4 + -2x5 + 4x6

Simplifying
f = -15x-1 + 30 + 16x + -32x2 + x3 + -2x4 + -2x5 + 4x6

Reorder the terms:
f = 30 + -15x-1 + 16x + -32x2 + x3 + -2x4 + -2x5 + 4x6

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