2x*(x+1)+6x-2*(1-x)=x*(1+x)

Solution for 2x*(x+1)+6x-2*(1-x)=x*(1+x) equation:

Simplifying
2x(x + 1) + 6x + -2(1 + -1x) = x(1 + x)

Reorder the terms:
2x(1 + x) + 6x + -2(1 + -1x) = x(1 + x)
(1 * 2x + x * 2x) + 6x + -2(1 + -1x) = x(1 + x)
(2x + 2x2) + 6x + -2(1 + -1x) = x(1 + x)
2x + 2x2 + 6x + (1 * -2 + -1x * -2) = x(1 + x)
2x + 2x2 + 6x + (-2 + 2x) = x(1 + x)

Reorder the terms:
-2 + 2x + 6x + 2x + 2x2 = x(1 + x)

Combine like terms: 2x + 6x = 8x
-2 + 8x + 2x + 2x2 = x(1 + x)

Combine like terms: 8x + 2x = 10x
-2 + 10x + 2x2 = x(1 + x)
-2 + 10x + 2x2 = (1 * x + x * x)
-2 + 10x + 2x2 = (1x + x2)

Solving
-2 + 10x + 2x2 = 1x + x2

Solving for variable 'x'.

Reorder the terms:
-2 + 10x + -1x + 2x2 + -1x2 = 1x + x2 + -1x + -1x2

Combine like terms: 10x + -1x = 9x
-2 + 9x + 2x2 + -1x2 = 1x + x2 + -1x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
-2 + 9x + 1x2 = 1x + x2 + -1x + -1x2

Reorder the terms:
-2 + 9x + 1x2 = 1x + -1x + x2 + -1x2

Combine like terms: 1x + -1x = 0
-2 + 9x + 1x2 = 0 + x2 + -1x2
-2 + 9x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-2 + 9x + 1x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 9x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + 9x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 9x + x2 = 0 + 2
9x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
9x + x2 = 2

The x term is 9x.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9x + 20.25 + x2 = 2 + 20.25

Reorder the terms:
20.25 + 9x + x2 = 2 + 20.25

Combine like terms: 2 + 20.25 = 22.25
20.25 + 9x + x2 = 22.25

Factor a perfect square on the left side:
(x + 4.5)(x + 4.5) = 22.25

Calculate the square root of the right side: 4.716990566

Break this problem into two subproblems by setting 
(x + 4.5) equal to 4.716990566 and -4.716990566.

Subproblem 1
x + 4.5 = 4.716990566

Simplifying
x + 4.5 = 4.716990566

Reorder the terms:
4.5 + x = 4.716990566

Solving
4.5 + x = 4.716990566

Solving for variable 'x'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = 4.716990566 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = 4.716990566 + -4.5
x = 4.716990566 + -4.5

Combine like terms: 4.716990566 + -4.5 = 0.216990566
x = 0.216990566

Simplifying
x = 0.216990566

Subproblem 2
x + 4.5 = -4.716990566

Simplifying
x + 4.5 = -4.716990566

Reorder the terms:
4.5 + x = -4.716990566

Solving
4.5 + x = -4.716990566

Solving for variable 'x'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = -4.716990566 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = -4.716990566 + -4.5
x = -4.716990566 + -4.5

Combine like terms: -4.716990566 + -4.5 = -9.216990566
x = -9.216990566

Simplifying
x = -9.216990566

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.216990566, -9.216990566}