f(x)=(x^2-4x-5)(x^2-8x+32)

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Solution for f(x)=(x^2-4x-5)(x^2-8x+32) equation: 


Simplifying
f(x) = (x2 + -4x + -5)(x2 + -8x + 32)

Multiply f * x
fx = (x2 + -4x + -5)(x2 + -8x + 32)

Reorder the terms:
fx = (-5 + -4x + x2)(x2 + -8x + 32)

Reorder the terms:
fx = (-5 + -4x + x2)(32 + -8x + x2)

Multiply (-5 + -4x + x2) * (32 + -8x + x2)
fx = (-5(32 + -8x + x2) + -4x * (32 + -8x + x2) + x2(32 + -8x + x2))
fx = ((32 * -5 + -8x * -5 + x2 * -5) + -4x * (32 + -8x + x2) + x2(32 + -8x + x2))
fx = ((-160 + 40x + -5x2) + -4x * (32 + -8x + x2) + x2(32 + -8x + x2))
fx = (-160 + 40x + -5x2 + (32 * -4x + -8x * -4x + x2 * -4x) + x2(32 + -8x + x2))
fx = (-160 + 40x + -5x2 + (-128x + 32x2 + -4x3) + x2(32 + -8x + x2))
fx = (-160 + 40x + -5x2 + -128x + 32x2 + -4x3 + (32 * x2 + -8x * x2 + x2 * x2))
fx = (-160 + 40x + -5x2 + -128x + 32x2 + -4x3 + (32x2 + -8x3 + x4))

Reorder the terms:
fx = (-160 + 40x + -128x + -5x2 + 32x2 + 32x2 + -4x3 + -8x3 + x4)

Combine like terms: 40x + -128x = -88x
fx = (-160 + -88x + -5x2 + 32x2 + 32x2 + -4x3 + -8x3 + x4)

Combine like terms: -5x2 + 32x2 = 27x2
fx = (-160 + -88x + 27x2 + 32x2 + -4x3 + -8x3 + x4)

Combine like terms: 27x2 + 32x2 = 59x2
fx = (-160 + -88x + 59x2 + -4x3 + -8x3 + x4)

Combine like terms: -4x3 + -8x3 = -12x3
fx = (-160 + -88x + 59x2 + -12x3 + x4)

Solving
fx = -160 + -88x + 59x2 + -12x3 + x4

Solving for variable 'f'.

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

Divide each side by 'x'.
f = -160x-1 + -88 + 59x + -12x2 + x3

Simplifying
f = -160x-1 + -88 + 59x + -12x2 + x3

Reorder the terms:
f = -88 + -160x-1 + 59x + -12x2 + x3

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