Cmin=(x+1)(x+2)(x+3)(x+4)+15

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Solution for Cmin=(x+1)(x+2)(x+3)(x+4)+15 equation: 


Simplifying
Cmin = (x + 1)(x + 2)(x + 3)(x + 4) + 15

Reorder the terms:
imnC = (1 + x)(x + 2)(x + 3)(x + 4) + 15

Reorder the terms:
imnC = (1 + x)(2 + x)(x + 3)(x + 4) + 15

Reorder the terms:
imnC = (1 + x)(2 + x)(3 + x)(x + 4) + 15

Reorder the terms:
imnC = (1 + x)(2 + x)(3 + x)(4 + x) + 15

Multiply (1 + x) * (2 + x)
imnC = (1(2 + x) + x(2 + x))(3 + x)(4 + x) + 15
imnC = ((2 * 1 + x * 1) + x(2 + x))(3 + x)(4 + x) + 15
imnC = ((2 + 1x) + x(2 + x))(3 + x)(4 + x) + 15
imnC = (2 + 1x + (2 * x + x * x))(3 + x)(4 + x) + 15
imnC = (2 + 1x + (2x + x2))(3 + x)(4 + x) + 15

Combine like terms: 1x + 2x = 3x
imnC = (2 + 3x + x2)(3 + x)(4 + x) + 15

Multiply (2 + 3x + x2) * (3 + x)
imnC = (2(3 + x) + 3x * (3 + x) + x2(3 + x))(4 + x) + 15
imnC = ((3 * 2 + x * 2) + 3x * (3 + x) + x2(3 + x))(4 + x) + 15
imnC = ((6 + 2x) + 3x * (3 + x) + x2(3 + x))(4 + x) + 15
imnC = (6 + 2x + (3 * 3x + x * 3x) + x2(3 + x))(4 + x) + 15
imnC = (6 + 2x + (9x + 3x2) + x2(3 + x))(4 + x) + 15
imnC = (6 + 2x + 9x + 3x2 + (3 * x2 + x * x2))(4 + x) + 15
imnC = (6 + 2x + 9x + 3x2 + (3x2 + x3))(4 + x) + 15

Combine like terms: 2x + 9x = 11x
imnC = (6 + 11x + 3x2 + 3x2 + x3)(4 + x) + 15

Combine like terms: 3x2 + 3x2 = 6x2
imnC = (6 + 11x + 6x2 + x3)(4 + x) + 15

Multiply (6 + 11x + 6x2 + x3) * (4 + x)
imnC = (6(4 + x) + 11x * (4 + x) + 6x2 * (4 + x) + x3(4 + x)) + 15
imnC = ((4 * 6 + x * 6) + 11x * (4 + x) + 6x2 * (4 + x) + x3(4 + x)) + 15
imnC = ((24 + 6x) + 11x * (4 + x) + 6x2 * (4 + x) + x3(4 + x)) + 15
imnC = (24 + 6x + (4 * 11x + x * 11x) + 6x2 * (4 + x) + x3(4 + x)) + 15
imnC = (24 + 6x + (44x + 11x2) + 6x2 * (4 + x) + x3(4 + x)) + 15
imnC = (24 + 6x + 44x + 11x2 + (4 * 6x2 + x * 6x2) + x3(4 + x)) + 15
imnC = (24 + 6x + 44x + 11x2 + (24x2 + 6x3) + x3(4 + x)) + 15
imnC = (24 + 6x + 44x + 11x2 + 24x2 + 6x3 + (4 * x3 + x * x3)) + 15
imnC = (24 + 6x + 44x + 11x2 + 24x2 + 6x3 + (4x3 + x4)) + 15

Combine like terms: 6x + 44x = 50x
imnC = (24 + 50x + 11x2 + 24x2 + 6x3 + 4x3 + x4) + 15

Combine like terms: 11x2 + 24x2 = 35x2
imnC = (24 + 50x + 35x2 + 6x3 + 4x3 + x4) + 15

Combine like terms: 6x3 + 4x3 = 10x3
imnC = (24 + 50x + 35x2 + 10x3 + x4) + 15

Reorder the terms:
imnC = 24 + 15 + 50x + 35x2 + 10x3 + x4

Combine like terms: 24 + 15 = 39
imnC = 39 + 50x + 35x2 + 10x3 + x4

Solving
imnC = 39 + 50x + 35x2 + 10x3 + x4

Solving for variable 'i'.

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

Divide each side by 'mnC'.
i = 39m-1n-1C-1 + 50m-1n-1xC-1 + 35m-1n-1x2C-1 + 10m-1n-1x3C-1 + m-1n-1x4C-1

Simplifying
i = 39m-1n-1C-1 + 50m-1n-1xC-1 + 35m-1n-1x2C-1 + 10m-1n-1x3C-1 + m-1n-1x4C-1

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