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

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


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

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

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

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

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

Combine like terms: -1x + 1x = 0
(1 + 0 + 1x2 + -1x2 + x3) + -1(x + -1)(x2 + x + 1) = 2(x + -2)
(1 + 1x2 + -1x2 + x3) + -1(x + -1)(x2 + x + 1) = 2(x + -2)

Combine like terms: 1x2 + -1x2 = 0
(1 + 0 + x3) + -1(x + -1)(x2 + x + 1) = 2(x + -2)
(1 + x3) + -1(x + -1)(x2 + x + 1) = 2(x + -2)

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

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

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

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

Combine like terms: -1x + 1x = 0
1 + x3 + -1(-1 + 0 + -1x2 + x2 + x3) = 2(x + -2)
1 + x3 + -1(-1 + -1x2 + x2 + x3) = 2(x + -2)

Combine like terms: -1x2 + x2 = 0
1 + x3 + -1(-1 + 0 + x3) = 2(x + -2)
1 + x3 + -1(-1 + x3) = 2(x + -2)
1 + x3 + (-1 * -1 + x3 * -1) = 2(x + -2)
1 + x3 + (1 + -1x3) = 2(x + -2)

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

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

Combine like terms: x3 + -1x3 = 0
2 + 0 = 2(x + -2)
2 = 2(x + -2)

Reorder the terms:
2 = 2(-2 + x)
2 = (-2 * 2 + x * 2)
2 = (-4 + 2x)

Solving
2 = -4 + 2x

Solving for variable 'x'.

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

Add '-2x' to each side of the equation.
2 + -2x = -4 + 2x + -2x

Combine like terms: 2x + -2x = 0
2 + -2x = -4 + 0
2 + -2x = -4

Add '-2' to each side of the equation.
2 + -2 + -2x = -4 + -2

Combine like terms: 2 + -2 = 0
0 + -2x = -4 + -2
-2x = -4 + -2

Combine like terms: -4 + -2 = -6
-2x = -6

Divide each side by '-2'.
x = 3

Simplifying
x = 3

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