f(x)=(6+4x+3x^2)*(2+4x+2x^2)

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Solution for f(x)=(6+4x+3x^2)*(2+4x+2x^2) equation: 


Simplifying
f(x) = (6 + 4x + 3x2)(2 + 4x + 2x2)

Multiply f * x
fx = (6 + 4x + 3x2)(2 + 4x + 2x2)

Multiply (6 + 4x + 3x2) * (2 + 4x + 2x2)
fx = (6(2 + 4x + 2x2) + 4x * (2 + 4x + 2x2) + 3x2 * (2 + 4x + 2x2))
fx = ((2 * 6 + 4x * 6 + 2x2 * 6) + 4x * (2 + 4x + 2x2) + 3x2 * (2 + 4x + 2x2))
fx = ((12 + 24x + 12x2) + 4x * (2 + 4x + 2x2) + 3x2 * (2 + 4x + 2x2))
fx = (12 + 24x + 12x2 + (2 * 4x + 4x * 4x + 2x2 * 4x) + 3x2 * (2 + 4x + 2x2))
fx = (12 + 24x + 12x2 + (8x + 16x2 + 8x3) + 3x2 * (2 + 4x + 2x2))
fx = (12 + 24x + 12x2 + 8x + 16x2 + 8x3 + (2 * 3x2 + 4x * 3x2 + 2x2 * 3x2))
fx = (12 + 24x + 12x2 + 8x + 16x2 + 8x3 + (6x2 + 12x3 + 6x4))

Reorder the terms:
fx = (12 + 24x + 8x + 12x2 + 16x2 + 6x2 + 8x3 + 12x3 + 6x4)

Combine like terms: 24x + 8x = 32x
fx = (12 + 32x + 12x2 + 16x2 + 6x2 + 8x3 + 12x3 + 6x4)

Combine like terms: 12x2 + 16x2 = 28x2
fx = (12 + 32x + 28x2 + 6x2 + 8x3 + 12x3 + 6x4)

Combine like terms: 28x2 + 6x2 = 34x2
fx = (12 + 32x + 34x2 + 8x3 + 12x3 + 6x4)

Combine like terms: 8x3 + 12x3 = 20x3
fx = (12 + 32x + 34x2 + 20x3 + 6x4)

Solving
fx = 12 + 32x + 34x2 + 20x3 + 6x4

Solving for variable 'f'.

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

Divide each side by 'x'.
f = 12x-1 + 32 + 34x + 20x2 + 6x3

Simplifying
f = 12x-1 + 32 + 34x + 20x2 + 6x3

Reorder the terms:
f = 32 + 12x-1 + 34x + 20x2 + 6x3

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