f(x)=a((x^2-8x+16)(x^2-4x+20))

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Solution for f(x)=a((x^2-8x+16)(x^2-4x+20)) equation: 


Simplifying
f(x) = a((x2 + -8x + 16)(x2 + -4x + 20))

Multiply f * x
fx = a((x2 + -8x + 16)(x2 + -4x + 20))

Reorder the terms:
fx = a((16 + -8x + x2)(x2 + -4x + 20))

Reorder the terms:
fx = a((16 + -8x + x2)(20 + -4x + x2))

Multiply (16 + -8x + x2) * (20 + -4x + x2)
fx = a((16(20 + -4x + x2) + -8x * (20 + -4x + x2) + x2(20 + -4x + x2)))
fx = a(((20 * 16 + -4x * 16 + x2 * 16) + -8x * (20 + -4x + x2) + x2(20 + -4x + x2)))
fx = a(((320 + -64x + 16x2) + -8x * (20 + -4x + x2) + x2(20 + -4x + x2)))
fx = a((320 + -64x + 16x2 + (20 * -8x + -4x * -8x + x2 * -8x) + x2(20 + -4x + x2)))
fx = a((320 + -64x + 16x2 + (-160x + 32x2 + -8x3) + x2(20 + -4x + x2)))
fx = a((320 + -64x + 16x2 + -160x + 32x2 + -8x3 + (20 * x2 + -4x * x2 + x2 * x2)))
fx = a((320 + -64x + 16x2 + -160x + 32x2 + -8x3 + (20x2 + -4x3 + x4)))

Reorder the terms:
fx = a((320 + -64x + -160x + 16x2 + 32x2 + 20x2 + -8x3 + -4x3 + x4))

Combine like terms: -64x + -160x = -224x
fx = a((320 + -224x + 16x2 + 32x2 + 20x2 + -8x3 + -4x3 + x4))

Combine like terms: 16x2 + 32x2 = 48x2
fx = a((320 + -224x + 48x2 + 20x2 + -8x3 + -4x3 + x4))

Combine like terms: 48x2 + 20x2 = 68x2
fx = a((320 + -224x + 68x2 + -8x3 + -4x3 + x4))

Combine like terms: -8x3 + -4x3 = -12x3
fx = a((320 + -224x + 68x2 + -12x3 + x4))
fx = (320 * a + -224x * a + 68x2 * a + -12x3 * a + x4 * a)
fx = (320a + -224ax + 68ax2 + -12ax3 + ax4)

Solving
fx = 320a + -224ax + 68ax2 + -12ax3 + ax4

Solving for variable 'f'.

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

Divide each side by 'x'.
f = 320ax-1 + -224a + 68ax + -12ax2 + ax3

Simplifying
f = 320ax-1 + -224a + 68ax + -12ax2 + ax3

Reorder the terms:
f = -224a + 320ax-1 + 68ax + -12ax2 + ax3

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