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

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


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

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

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

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

Combine like terms: 1x + 2x = 3x
x(2 + 3x + x2) + -1(x + 1)(x + -2)(x + 3) = x + -1
(2 * x + 3x * x + x2 * x) + -1(x + 1)(x + -2)(x + 3) = x + -1
(2x + 3x2 + x3) + -1(x + 1)(x + -2)(x + 3) = x + -1

Reorder the terms:
2x + 3x2 + x3 + -1(1 + x)(x + -2)(x + 3) = x + -1

Reorder the terms:
2x + 3x2 + x3 + -1(1 + x)(-2 + x)(x + 3) = x + -1

Reorder the terms:
2x + 3x2 + x3 + -1(1 + x)(-2 + x)(3 + x) = x + -1

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

Combine like terms: 1x + -2x = -1x
2x + 3x2 + x3 + -1(-2 + -1x + x2)(3 + x) = x + -1

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

Combine like terms: -2x + -3x = -5x
2x + 3x2 + x3 + -1(-6 + -5x + -1x2 + 3x2 + x3) = x + -1

Combine like terms: -1x2 + 3x2 = 2x2
2x + 3x2 + x3 + -1(-6 + -5x + 2x2 + x3) = x + -1
2x + 3x2 + x3 + (-6 * -1 + -5x * -1 + 2x2 * -1 + x3 * -1) = x + -1
2x + 3x2 + x3 + (6 + 5x + -2x2 + -1x3) = x + -1

Reorder the terms:
6 + 2x + 5x + 3x2 + -2x2 + x3 + -1x3 = x + -1

Combine like terms: 2x + 5x = 7x
6 + 7x + 3x2 + -2x2 + x3 + -1x3 = x + -1

Combine like terms: 3x2 + -2x2 = 1x2
6 + 7x + 1x2 + x3 + -1x3 = x + -1

Combine like terms: x3 + -1x3 = 0
6 + 7x + 1x2 + 0 = x + -1
6 + 7x + 1x2 = x + -1

Reorder the terms:
6 + 7x + 1x2 = -1 + x

Solving
6 + 7x + 1x2 = -1 + x

Solving for variable 'x'.

Reorder the terms:
6 + 1 + 7x + -1x + 1x2 = -1 + x + 1 + -1x

Combine like terms: 6 + 1 = 7
7 + 7x + -1x + 1x2 = -1 + x + 1 + -1x

Combine like terms: 7x + -1x = 6x
7 + 6x + 1x2 = -1 + x + 1 + -1x

Reorder the terms:
7 + 6x + 1x2 = -1 + 1 + x + -1x

Combine like terms: -1 + 1 = 0
7 + 6x + 1x2 = 0 + x + -1x
7 + 6x + 1x2 = x + -1x

Combine like terms: x + -1x = 0
7 + 6x + 1x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-7' to each side of the equation.
7 + 6x + -7 + x2 = 0 + -7

Reorder the terms:
7 + -7 + 6x + x2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 6x + x2 = 0 + -7
6x + x2 = 0 + -7

Combine like terms: 0 + -7 = -7
6x + x2 = -7

The x term is 6x.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x + 9 + x2 = -7 + 9

Reorder the terms:
9 + 6x + x2 = -7 + 9

Combine like terms: -7 + 9 = 2
9 + 6x + x2 = 2

Factor a perfect square on the left side:
(x + 3)(x + 3) = 2

Calculate the square root of the right side: 1.414213562

Break this problem into two subproblems by setting 
(x + 3) equal to 1.414213562 and -1.414213562.


Subproblem 1
x + 3 = 1.414213562

Simplifying
x + 3 = 1.414213562

Reorder the terms:
3 + x = 1.414213562

Solving
3 + x = 1.414213562

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = 1.414213562 + -3

Combine like terms: 3 + -3 = 0
0 + x = 1.414213562 + -3
x = 1.414213562 + -3

Combine like terms: 1.414213562 + -3 = -1.585786438
x = -1.585786438

Simplifying
x = -1.585786438


Subproblem 2
x + 3 = -1.414213562

Simplifying
x + 3 = -1.414213562

Reorder the terms:
3 + x = -1.414213562

Solving
3 + x = -1.414213562

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = -1.414213562 + -3

Combine like terms: 3 + -3 = 0
0 + x = -1.414213562 + -3
x = -1.414213562 + -3

Combine like terms: -1.414213562 + -3 = -4.414213562
x = -4.414213562

Simplifying
x = -4.414213562


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.585786438, -4.414213562}

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