x(x+1)(x+2)(x+3)+1=(x^2+3x+1)(x^2+3x+1)

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


Simplifying
x(x + 1)(x + 2)(x + 3) + 1 = (x2 + 3x + 1)(x2 + 3x + 1)

Reorder the terms:
x(1 + x)(x + 2)(x + 3) + 1 = (x2 + 3x + 1)(x2 + 3x + 1)

Reorder the terms:
x(1 + x)(2 + x)(x + 3) + 1 = (x2 + 3x + 1)(x2 + 3x + 1)

Reorder the terms:
x(1 + x)(2 + x)(3 + x) + 1 = (x2 + 3x + 1)(x2 + 3x + 1)

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

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

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

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

Combine like terms: 3x2 + 3x2 = 6x2
x(6 + 11x + 6x2 + x3) + 1 = (x2 + 3x + 1)(x2 + 3x + 1)
(6 * x + 11x * x + 6x2 * x + x3 * x) + 1 = (x2 + 3x + 1)(x2 + 3x + 1)
(6x + 11x2 + 6x3 + x4) + 1 = (x2 + 3x + 1)(x2 + 3x + 1)

Reorder the terms:
1 + 6x + 11x2 + 6x3 + x4 = (x2 + 3x + 1)(x2 + 3x + 1)

Reorder the terms:
1 + 6x + 11x2 + 6x3 + x4 = (1 + 3x + x2)(x2 + 3x + 1)

Reorder the terms:
1 + 6x + 11x2 + 6x3 + x4 = (1 + 3x + x2)(1 + 3x + x2)

Multiply (1 + 3x + x2) * (1 + 3x + x2)
1 + 6x + 11x2 + 6x3 + x4 = (1(1 + 3x + x2) + 3x * (1 + 3x + x2) + x2(1 + 3x + x2))
1 + 6x + 11x2 + 6x3 + x4 = ((1 * 1 + 3x * 1 + x2 * 1) + 3x * (1 + 3x + x2) + x2(1 + 3x + x2))
1 + 6x + 11x2 + 6x3 + x4 = ((1 + 3x + 1x2) + 3x * (1 + 3x + x2) + x2(1 + 3x + x2))
1 + 6x + 11x2 + 6x3 + x4 = (1 + 3x + 1x2 + (1 * 3x + 3x * 3x + x2 * 3x) + x2(1 + 3x + x2))
1 + 6x + 11x2 + 6x3 + x4 = (1 + 3x + 1x2 + (3x + 9x2 + 3x3) + x2(1 + 3x + x2))
1 + 6x + 11x2 + 6x3 + x4 = (1 + 3x + 1x2 + 3x + 9x2 + 3x3 + (1 * x2 + 3x * x2 + x2 * x2))
1 + 6x + 11x2 + 6x3 + x4 = (1 + 3x + 1x2 + 3x + 9x2 + 3x3 + (1x2 + 3x3 + x4))

Reorder the terms:
1 + 6x + 11x2 + 6x3 + x4 = (1 + 3x + 3x + 1x2 + 9x2 + 1x2 + 3x3 + 3x3 + x4)

Combine like terms: 3x + 3x = 6x
1 + 6x + 11x2 + 6x3 + x4 = (1 + 6x + 1x2 + 9x2 + 1x2 + 3x3 + 3x3 + x4)

Combine like terms: 1x2 + 9x2 = 10x2
1 + 6x + 11x2 + 6x3 + x4 = (1 + 6x + 10x2 + 1x2 + 3x3 + 3x3 + x4)

Combine like terms: 10x2 + 1x2 = 11x2
1 + 6x + 11x2 + 6x3 + x4 = (1 + 6x + 11x2 + 3x3 + 3x3 + x4)

Combine like terms: 3x3 + 3x3 = 6x3
1 + 6x + 11x2 + 6x3 + x4 = (1 + 6x + 11x2 + 6x3 + x4)

Add '-1' to each side of the equation.
1 + 6x + 11x2 + 6x3 + -1 + x4 = 1 + 6x + 11x2 + 6x3 + -1 + x4

Reorder the terms:
1 + -1 + 6x + 11x2 + 6x3 + x4 = 1 + 6x + 11x2 + 6x3 + -1 + x4

Combine like terms: 1 + -1 = 0
0 + 6x + 11x2 + 6x3 + x4 = 1 + 6x + 11x2 + 6x3 + -1 + x4
6x + 11x2 + 6x3 + x4 = 1 + 6x + 11x2 + 6x3 + -1 + x4

Reorder the terms:
6x + 11x2 + 6x3 + x4 = 1 + -1 + 6x + 11x2 + 6x3 + x4

Combine like terms: 1 + -1 = 0
6x + 11x2 + 6x3 + x4 = 0 + 6x + 11x2 + 6x3 + x4
6x + 11x2 + 6x3 + x4 = 6x + 11x2 + 6x3 + x4

Add '-6x' to each side of the equation.
6x + 11x2 + 6x3 + -6x + x4 = 6x + 11x2 + 6x3 + -6x + x4

Reorder the terms:
6x + -6x + 11x2 + 6x3 + x4 = 6x + 11x2 + 6x3 + -6x + x4

Combine like terms: 6x + -6x = 0
0 + 11x2 + 6x3 + x4 = 6x + 11x2 + 6x3 + -6x + x4
11x2 + 6x3 + x4 = 6x + 11x2 + 6x3 + -6x + x4

Reorder the terms:
11x2 + 6x3 + x4 = 6x + -6x + 11x2 + 6x3 + x4

Combine like terms: 6x + -6x = 0
11x2 + 6x3 + x4 = 0 + 11x2 + 6x3 + x4
11x2 + 6x3 + x4 = 11x2 + 6x3 + x4

Add '-11x2' to each side of the equation.
11x2 + 6x3 + -11x2 + x4 = 11x2 + 6x3 + -11x2 + x4

Reorder the terms:
11x2 + -11x2 + 6x3 + x4 = 11x2 + 6x3 + -11x2 + x4

Combine like terms: 11x2 + -11x2 = 0
0 + 6x3 + x4 = 11x2 + 6x3 + -11x2 + x4
6x3 + x4 = 11x2 + 6x3 + -11x2 + x4

Reorder the terms:
6x3 + x4 = 11x2 + -11x2 + 6x3 + x4

Combine like terms: 11x2 + -11x2 = 0
6x3 + x4 = 0 + 6x3 + x4
6x3 + x4 = 6x3 + x4

Add '-6x3' to each side of the equation.
6x3 + -6x3 + x4 = 6x3 + -6x3 + x4

Combine like terms: 6x3 + -6x3 = 0
0 + x4 = 6x3 + -6x3 + x4
x4 = 6x3 + -6x3 + x4

Combine like terms: 6x3 + -6x3 = 0
x4 = 0 + x4
x4 = x4

Add '-1x4' to each side of the equation.
x4 + -1x4 = x4 + -1x4

Combine like terms: x4 + -1x4 = 0
0 = x4 + -1x4

Combine like terms: x4 + -1x4 = 0
0 = 0

Solving
0 = 0

Couldn't find a variable to solve for.

This equation is an identity, all real numbers are solutions.

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