(x+10)(x+2)(x+1)+x(x+2)(x+1)=x(x+10)(x+1)+x(x+10)(x+2)

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Solution for (x+10)(x+2)(x+1)+x(x+2)(x+1)=x(x+10)(x+1)+x(x+10)(x+2) equation: 


Simplifying
(x + 10)(x + 2)(x + 1) + x(x + 2)(x + 1) = x(x + 10)(x + 1) + x(x + 10)(x + 2)

Reorder the terms:
(10 + x)(x + 2)(x + 1) + x(x + 2)(x + 1) = x(x + 10)(x + 1) + x(x + 10)(x + 2)

Reorder the terms:
(10 + x)(2 + x)(x + 1) + x(x + 2)(x + 1) = x(x + 10)(x + 1) + x(x + 10)(x + 2)

Reorder the terms:
(10 + x)(2 + x)(1 + x) + x(x + 2)(x + 1) = x(x + 10)(x + 1) + x(x + 10)(x + 2)

Multiply (10 + x) * (2 + x)
(10(2 + x) + x(2 + x))(1 + x) + x(x + 2)(x + 1) = x(x + 10)(x + 1) + x(x + 10)(x + 2)
((2 * 10 + x * 10) + x(2 + x))(1 + x) + x(x + 2)(x + 1) = x(x + 10)(x + 1) + x(x + 10)(x + 2)
((20 + 10x) + x(2 + x))(1 + x) + x(x + 2)(x + 1) = x(x + 10)(x + 1) + x(x + 10)(x + 2)
(20 + 10x + (2 * x + x * x))(1 + x) + x(x + 2)(x + 1) = x(x + 10)(x + 1) + x(x + 10)(x + 2)
(20 + 10x + (2x + x2))(1 + x) + x(x + 2)(x + 1) = x(x + 10)(x + 1) + x(x + 10)(x + 2)

Combine like terms: 10x + 2x = 12x
(20 + 12x + x2)(1 + x) + x(x + 2)(x + 1) = x(x + 10)(x + 1) + x(x + 10)(x + 2)

Multiply (20 + 12x + x2) * (1 + x)
(20(1 + x) + 12x * (1 + x) + x2(1 + x)) + x(x + 2)(x + 1) = x(x + 10)(x + 1) + x(x + 10)(x + 2)
((1 * 20 + x * 20) + 12x * (1 + x) + x2(1 + x)) + x(x + 2)(x + 1) = x(x + 10)(x + 1) + x(x + 10)(x + 2)
((20 + 20x) + 12x * (1 + x) + x2(1 + x)) + x(x + 2)(x + 1) = x(x + 10)(x + 1) + x(x + 10)(x + 2)
(20 + 20x + (1 * 12x + x * 12x) + x2(1 + x)) + x(x + 2)(x + 1) = x(x + 10)(x + 1) + x(x + 10)(x + 2)
(20 + 20x + (12x + 12x2) + x2(1 + x)) + x(x + 2)(x + 1) = x(x + 10)(x + 1) + x(x + 10)(x + 2)
(20 + 20x + 12x + 12x2 + (1 * x2 + x * x2)) + x(x + 2)(x + 1) = x(x + 10)(x + 1) + x(x + 10)(x + 2)
(20 + 20x + 12x + 12x2 + (1x2 + x3)) + x(x + 2)(x + 1) = x(x + 10)(x + 1) + x(x + 10)(x + 2)

Combine like terms: 20x + 12x = 32x
(20 + 32x + 12x2 + 1x2 + x3) + x(x + 2)(x + 1) = x(x + 10)(x + 1) + x(x + 10)(x + 2)

Combine like terms: 12x2 + 1x2 = 13x2
(20 + 32x + 13x2 + x3) + x(x + 2)(x + 1) = x(x + 10)(x + 1) + x(x + 10)(x + 2)

Reorder the terms:
20 + 32x + 13x2 + x3 + x(2 + x)(x + 1) = x(x + 10)(x + 1) + x(x + 10)(x + 2)

Reorder the terms:
20 + 32x + 13x2 + x3 + x(2 + x)(1 + x) = x(x + 10)(x + 1) + x(x + 10)(x + 2)

Multiply (2 + x) * (1 + x)
20 + 32x + 13x2 + x3 + x(2(1 + x) + x(1 + x)) = x(x + 10)(x + 1) + x(x + 10)(x + 2)
20 + 32x + 13x2 + x3 + x((1 * 2 + x * 2) + x(1 + x)) = x(x + 10)(x + 1) + x(x + 10)(x + 2)
20 + 32x + 13x2 + x3 + x((2 + 2x) + x(1 + x)) = x(x + 10)(x + 1) + x(x + 10)(x + 2)
20 + 32x + 13x2 + x3 + x(2 + 2x + (1 * x + x * x)) = x(x + 10)(x + 1) + x(x + 10)(x + 2)
20 + 32x + 13x2 + x3 + x(2 + 2x + (1x + x2)) = x(x + 10)(x + 1) + x(x + 10)(x + 2)

Combine like terms: 2x + 1x = 3x
20 + 32x + 13x2 + x3 + x(2 + 3x + x2) = x(x + 10)(x + 1) + x(x + 10)(x + 2)
20 + 32x + 13x2 + x3 + (2 * x + 3x * x + x2 * x) = x(x + 10)(x + 1) + x(x + 10)(x + 2)
20 + 32x + 13x2 + x3 + (2x + 3x2 + x3) = x(x + 10)(x + 1) + x(x + 10)(x + 2)

Reorder the terms:
20 + 32x + 2x + 13x2 + 3x2 + x3 + x3 = x(x + 10)(x + 1) + x(x + 10)(x + 2)

Combine like terms: 32x + 2x = 34x
20 + 34x + 13x2 + 3x2 + x3 + x3 = x(x + 10)(x + 1) + x(x + 10)(x + 2)

Combine like terms: 13x2 + 3x2 = 16x2
20 + 34x + 16x2 + x3 + x3 = x(x + 10)(x + 1) + x(x + 10)(x + 2)

Combine like terms: x3 + x3 = 2x3
20 + 34x + 16x2 + 2x3 = x(x + 10)(x + 1) + x(x + 10)(x + 2)

Reorder the terms:
20 + 34x + 16x2 + 2x3 = x(10 + x)(x + 1) + x(x + 10)(x + 2)

Reorder the terms:
20 + 34x + 16x2 + 2x3 = x(10 + x)(1 + x) + x(x + 10)(x + 2)

Multiply (10 + x) * (1 + x)
20 + 34x + 16x2 + 2x3 = x(10(1 + x) + x(1 + x)) + x(x + 10)(x + 2)
20 + 34x + 16x2 + 2x3 = x((1 * 10 + x * 10) + x(1 + x)) + x(x + 10)(x + 2)
20 + 34x + 16x2 + 2x3 = x((10 + 10x) + x(1 + x)) + x(x + 10)(x + 2)
20 + 34x + 16x2 + 2x3 = x(10 + 10x + (1 * x + x * x)) + x(x + 10)(x + 2)
20 + 34x + 16x2 + 2x3 = x(10 + 10x + (1x + x2)) + x(x + 10)(x + 2)

Combine like terms: 10x + 1x = 11x
20 + 34x + 16x2 + 2x3 = x(10 + 11x + x2) + x(x + 10)(x + 2)
20 + 34x + 16x2 + 2x3 = (10 * x + 11x * x + x2 * x) + x(x + 10)(x + 2)
20 + 34x + 16x2 + 2x3 = (10x + 11x2 + x3) + x(x + 10)(x + 2)

Reorder the terms:
20 + 34x + 16x2 + 2x3 = 10x + 11x2 + x3 + x(10 + x)(x + 2)

Reorder the terms:
20 + 34x + 16x2 + 2x3 = 10x + 11x2 + x3 + x(10 + x)(2 + x)

Multiply (10 + x) * (2 + x)
20 + 34x + 16x2 + 2x3 = 10x + 11x2 + x3 + x(10(2 + x) + x(2 + x))
20 + 34x + 16x2 + 2x3 = 10x + 11x2 + x3 + x((2 * 10 + x * 10) + x(2 + x))
20 + 34x + 16x2 + 2x3 = 10x + 11x2 + x3 + x((20 + 10x) + x(2 + x))
20 + 34x + 16x2 + 2x3 = 10x + 11x2 + x3 + x(20 + 10x + (2 * x + x * x))
20 + 34x + 16x2 + 2x3 = 10x + 11x2 + x3 + x(20 + 10x + (2x + x2))

Combine like terms: 10x + 2x = 12x
20 + 34x + 16x2 + 2x3 = 10x + 11x2 + x3 + x(20 + 12x + x2)
20 + 34x + 16x2 + 2x3 = 10x + 11x2 + x3 + (20 * x + 12x * x + x2 * x)
20 + 34x + 16x2 + 2x3 = 10x + 11x2 + x3 + (20x + 12x2 + x3)

Reorder the terms:
20 + 34x + 16x2 + 2x3 = 10x + 20x + 11x2 + 12x2 + x3 + x3

Combine like terms: 10x + 20x = 30x
20 + 34x + 16x2 + 2x3 = 30x + 11x2 + 12x2 + x3 + x3

Combine like terms: 11x2 + 12x2 = 23x2
20 + 34x + 16x2 + 2x3 = 30x + 23x2 + x3 + x3

Combine like terms: x3 + x3 = 2x3
20 + 34x + 16x2 + 2x3 = 30x + 23x2 + 2x3

Add '-2x3' to each side of the equation.
20 + 34x + 16x2 + 2x3 + -2x3 = 30x + 23x2 + 2x3 + -2x3

Combine like terms: 2x3 + -2x3 = 0
20 + 34x + 16x2 + 0 = 30x + 23x2 + 2x3 + -2x3
20 + 34x + 16x2 = 30x + 23x2 + 2x3 + -2x3

Combine like terms: 2x3 + -2x3 = 0
20 + 34x + 16x2 = 30x + 23x2 + 0
20 + 34x + 16x2 = 30x + 23x2

Solving
20 + 34x + 16x2 = 30x + 23x2

Solving for variable 'x'.

Reorder the terms:
20 + 34x + -30x + 16x2 + -23x2 = 30x + 23x2 + -30x + -23x2

Combine like terms: 34x + -30x = 4x
20 + 4x + 16x2 + -23x2 = 30x + 23x2 + -30x + -23x2

Combine like terms: 16x2 + -23x2 = -7x2
20 + 4x + -7x2 = 30x + 23x2 + -30x + -23x2

Reorder the terms:
20 + 4x + -7x2 = 30x + -30x + 23x2 + -23x2

Combine like terms: 30x + -30x = 0
20 + 4x + -7x2 = 0 + 23x2 + -23x2
20 + 4x + -7x2 = 23x2 + -23x2

Combine like terms: 23x2 + -23x2 = 0
20 + 4x + -7x2 = 0

Factor a trinomial.
(2 + -1x)(10 + 7x) = 0


Subproblem 1
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2

Subproblem 2
Set the factor '(10 + 7x)' equal to zero and attempt to solve:

Simplifying
10 + 7x = 0

Solving
10 + 7x = 0

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

Add '-10' to each side of the equation.
10 + -10 + 7x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + 7x = 0 + -10
7x = 0 + -10

Combine like terms: 0 + -10 = -10
7x = -10

Divide each side by '7'.
x = -1.428571429

Simplifying
x = -1.428571429
Solution
x = {2, -1.428571429}

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