f(x)=4x(x^2-4x+4)(x^2-32x+256)

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Solution for f(x)=4x(x^2-4x+4)(x^2-32x+256) equation: 


Simplifying
f(x) = 4x(x2 + -4x + 4)(x2 + -32x + 256)

Multiply f * x
fx = 4x(x2 + -4x + 4)(x2 + -32x + 256)

Reorder the terms:
fx = 4x(4 + -4x + x2)(x2 + -32x + 256)

Reorder the terms:
fx = 4x(4 + -4x + x2)(256 + -32x + x2)

Multiply (4 + -4x + x2) * (256 + -32x + x2)
fx = 4x(4(256 + -32x + x2) + -4x * (256 + -32x + x2) + x2(256 + -32x + x2))
fx = 4x((256 * 4 + -32x * 4 + x2 * 4) + -4x * (256 + -32x + x2) + x2(256 + -32x + x2))
fx = 4x((1024 + -128x + 4x2) + -4x * (256 + -32x + x2) + x2(256 + -32x + x2))
fx = 4x(1024 + -128x + 4x2 + (256 * -4x + -32x * -4x + x2 * -4x) + x2(256 + -32x + x2))
fx = 4x(1024 + -128x + 4x2 + (-1024x + 128x2 + -4x3) + x2(256 + -32x + x2))
fx = 4x(1024 + -128x + 4x2 + -1024x + 128x2 + -4x3 + (256 * x2 + -32x * x2 + x2 * x2))
fx = 4x(1024 + -128x + 4x2 + -1024x + 128x2 + -4x3 + (256x2 + -32x3 + x4))

Reorder the terms:
fx = 4x(1024 + -128x + -1024x + 4x2 + 128x2 + 256x2 + -4x3 + -32x3 + x4)

Combine like terms: -128x + -1024x = -1152x
fx = 4x(1024 + -1152x + 4x2 + 128x2 + 256x2 + -4x3 + -32x3 + x4)

Combine like terms: 4x2 + 128x2 = 132x2
fx = 4x(1024 + -1152x + 132x2 + 256x2 + -4x3 + -32x3 + x4)

Combine like terms: 132x2 + 256x2 = 388x2
fx = 4x(1024 + -1152x + 388x2 + -4x3 + -32x3 + x4)

Combine like terms: -4x3 + -32x3 = -36x3
fx = 4x(1024 + -1152x + 388x2 + -36x3 + x4)
fx = (1024 * 4x + -1152x * 4x + 388x2 * 4x + -36x3 * 4x + x4 * 4x)
fx = (4096x + -4608x2 + 1552x3 + -144x4 + 4x5)

Solving
fx = 4096x + -4608x2 + 1552x3 + -144x4 + 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 = 4096 + -4608x + 1552x2 + -144x3 + 4x4

Simplifying
f = 4096 + -4608x + 1552x2 + -144x3 + 4x4

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