(x+1)(x+2)(x+3)(x+4)+1=0

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Solution for (x+1)(x+2)(x+3)(x+4)+1=0 equation: 


Simplifying
(x + 1)(x + 2)(x + 3)(x + 4) + 1 = 0

Reorder the terms:
(1 + x)(x + 2)(x + 3)(x + 4) + 1 = 0

Reorder the terms:
(1 + x)(2 + x)(x + 3)(x + 4) + 1 = 0

Reorder the terms:
(1 + x)(2 + x)(3 + x)(x + 4) + 1 = 0

Reorder the terms:
(1 + x)(2 + x)(3 + x)(4 + x) + 1 = 0

Multiply (1 + x) * (2 + x)
(1(2 + x) + x(2 + x))(3 + x)(4 + x) + 1 = 0
((2 * 1 + x * 1) + x(2 + x))(3 + x)(4 + x) + 1 = 0
((2 + 1x) + x(2 + x))(3 + x)(4 + x) + 1 = 0
(2 + 1x + (2 * x + x * x))(3 + x)(4 + x) + 1 = 0
(2 + 1x + (2x + x2))(3 + x)(4 + x) + 1 = 0

Combine like terms: 1x + 2x = 3x
(2 + 3x + x2)(3 + x)(4 + x) + 1 = 0

Multiply (2 + 3x + x2) * (3 + x)
(2(3 + x) + 3x * (3 + x) + x2(3 + x))(4 + x) + 1 = 0
((3 * 2 + x * 2) + 3x * (3 + x) + x2(3 + x))(4 + x) + 1 = 0
((6 + 2x) + 3x * (3 + x) + x2(3 + x))(4 + x) + 1 = 0
(6 + 2x + (3 * 3x + x * 3x) + x2(3 + x))(4 + x) + 1 = 0
(6 + 2x + (9x + 3x2) + x2(3 + x))(4 + x) + 1 = 0
(6 + 2x + 9x + 3x2 + (3 * x2 + x * x2))(4 + x) + 1 = 0
(6 + 2x + 9x + 3x2 + (3x2 + x3))(4 + x) + 1 = 0

Combine like terms: 2x + 9x = 11x
(6 + 11x + 3x2 + 3x2 + x3)(4 + x) + 1 = 0

Combine like terms: 3x2 + 3x2 = 6x2
(6 + 11x + 6x2 + x3)(4 + x) + 1 = 0

Multiply (6 + 11x + 6x2 + x3) * (4 + x)
(6(4 + x) + 11x * (4 + x) + 6x2 * (4 + x) + x3(4 + x)) + 1 = 0
((4 * 6 + x * 6) + 11x * (4 + x) + 6x2 * (4 + x) + x3(4 + x)) + 1 = 0
((24 + 6x) + 11x * (4 + x) + 6x2 * (4 + x) + x3(4 + x)) + 1 = 0
(24 + 6x + (4 * 11x + x * 11x) + 6x2 * (4 + x) + x3(4 + x)) + 1 = 0
(24 + 6x + (44x + 11x2) + 6x2 * (4 + x) + x3(4 + x)) + 1 = 0
(24 + 6x + 44x + 11x2 + (4 * 6x2 + x * 6x2) + x3(4 + x)) + 1 = 0
(24 + 6x + 44x + 11x2 + (24x2 + 6x3) + x3(4 + x)) + 1 = 0
(24 + 6x + 44x + 11x2 + 24x2 + 6x3 + (4 * x3 + x * x3)) + 1 = 0
(24 + 6x + 44x + 11x2 + 24x2 + 6x3 + (4x3 + x4)) + 1 = 0

Combine like terms: 6x + 44x = 50x
(24 + 50x + 11x2 + 24x2 + 6x3 + 4x3 + x4) + 1 = 0

Combine like terms: 11x2 + 24x2 = 35x2
(24 + 50x + 35x2 + 6x3 + 4x3 + x4) + 1 = 0

Combine like terms: 6x3 + 4x3 = 10x3
(24 + 50x + 35x2 + 10x3 + x4) + 1 = 0

Reorder the terms:
24 + 1 + 50x + 35x2 + 10x3 + x4 = 0

Combine like terms: 24 + 1 = 25
25 + 50x + 35x2 + 10x3 + x4 = 0

Solving
25 + 50x + 35x2 + 10x3 + x4 = 0

Solving for variable 'x'.

The solution to this equation could not be determined.

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