f(x)=(x^3+4x^2-5)(x^4+8)

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Solution for f(x)=(x^3+4x^2-5)(x^4+8) equation: 


Simplifying
f(x) = (x3 + 4x2 + -5)(x4 + 8)

Multiply f * x
fx = (x3 + 4x2 + -5)(x4 + 8)

Reorder the terms:
fx = (-5 + 4x2 + x3)(x4 + 8)

Reorder the terms:
fx = (-5 + 4x2 + x3)(8 + x4)

Multiply (-5 + 4x2 + x3) * (8 + x4)
fx = (-5(8 + x4) + 4x2 * (8 + x4) + x3(8 + x4))
fx = ((8 * -5 + x4 * -5) + 4x2 * (8 + x4) + x3(8 + x4))
fx = ((-40 + -5x4) + 4x2 * (8 + x4) + x3(8 + x4))
fx = (-40 + -5x4 + (8 * 4x2 + x4 * 4x2) + x3(8 + x4))
fx = (-40 + -5x4 + (32x2 + 4x6) + x3(8 + x4))
fx = (-40 + -5x4 + 32x2 + 4x6 + (8 * x3 + x4 * x3))
fx = (-40 + -5x4 + 32x2 + 4x6 + (8x3 + x7))

Reorder the terms:
fx = (-40 + 32x2 + 8x3 + -5x4 + 4x6 + x7)
fx = (-40 + 32x2 + 8x3 + -5x4 + 4x6 + x7)

Solving
fx = -40 + 32x2 + 8x3 + -5x4 + 4x6 + x7

Solving for variable 'f'.

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

Divide each side by 'x'.
f = -40x-1 + 32x + 8x2 + -5x3 + 4x5 + x6

Simplifying
f = -40x-1 + 32x + 8x2 + -5x3 + 4x5 + x6

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