6x-6=2(x+1)4x-8

Solution for 6x-6=2(x+1)4x-8 equation:

Simplifying
6x + -6 = 2(x + 1) * 4x + -8

Reorder the terms:
-6 + 6x = 2(x + 1) * 4x + -8

Reorder the terms:
-6 + 6x = 2(1 + x) * 4x + -8

Reorder the terms for easier multiplication:
-6 + 6x = 2 * 4x(1 + x) + -8

Multiply 2 * 4
-6 + 6x = 8x(1 + x) + -8
-6 + 6x = (1 * 8x + x * 8x) + -8
-6 + 6x = (8x + 8x2) + -8

Reorder the terms:
-6 + 6x = -8 + 8x + 8x2

Solving
-6 + 6x = -8 + 8x + 8x2

Solving for variable 'x'.

Reorder the terms:
-6 + 8 + 6x + -8x + -8x2 = -8 + 8x + 8x2 + 8 + -8x + -8x2

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

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

Reorder the terms:
2 + -2x + -8x2 = -8 + 8 + 8x + -8x + 8x2 + -8x2

Combine like terms: -8 + 8 = 0
2 + -2x + -8x2 = 0 + 8x + -8x + 8x2 + -8x2
2 + -2x + -8x2 = 8x + -8x + 8x2 + -8x2

Combine like terms: 8x + -8x = 0
2 + -2x + -8x2 = 0 + 8x2 + -8x2
2 + -2x + -8x2 = 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
2 + -2x + -8x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + -1x + -4x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(1 + -1x + -4x2)' equal to zero and attempt to solve:

Simplifying
1 + -1x + -4x2 = 0

Solving
1 + -1x + -4x2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-0.25 + 0.25x + x2 = 0

Move the constant term to the right:

Add '0.25' to each side of the equation.
-0.25 + 0.25x + 0.25 + x2 = 0 + 0.25

Reorder the terms:
-0.25 + 0.25 + 0.25x + x2 = 0 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + 0.25x + x2 = 0 + 0.25
0.25x + x2 = 0 + 0.25

Combine like terms: 0 + 0.25 = 0.25
0.25x + x2 = 0.25

The x term is 0.25x.  Take half its coefficient (0.125).
Square it (0.015625) and add it to both sides.

Add '0.015625' to each side of the equation.
0.25x + 0.015625 + x2 = 0.25 + 0.015625

Reorder the terms:
0.015625 + 0.25x + x2 = 0.25 + 0.015625

Combine like terms: 0.25 + 0.015625 = 0.265625
0.015625 + 0.25x + x2 = 0.265625

Factor a perfect square on the left side:
(x + 0.125)(x + 0.125) = 0.265625

Calculate the square root of the right side: 0.515388203

Break this problem into two subproblems by setting 
(x + 0.125) equal to 0.515388203 and -0.515388203.

Subproblem 1
x + 0.125 = 0.515388203

Simplifying
x + 0.125 = 0.515388203

Reorder the terms:
0.125 + x = 0.515388203

Solving
0.125 + x = 0.515388203

Solving for variable 'x'.

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

Add '-0.125' to each side of the equation.
0.125 + -0.125 + x = 0.515388203 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + x = 0.515388203 + -0.125
x = 0.515388203 + -0.125

Combine like terms: 0.515388203 + -0.125 = 0.390388203
x = 0.390388203

Simplifying
x = 0.390388203

Subproblem 2
x + 0.125 = -0.515388203

Simplifying
x + 0.125 = -0.515388203

Reorder the terms:
0.125 + x = -0.515388203

Solving
0.125 + x = -0.515388203

Solving for variable 'x'.

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

Add '-0.125' to each side of the equation.
0.125 + -0.125 + x = -0.515388203 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + x = -0.515388203 + -0.125
x = -0.515388203 + -0.125

Combine like terms: -0.515388203 + -0.125 = -0.640388203
x = -0.640388203

Simplifying
x = -0.640388203

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.390388203, -0.640388203}
Solution
x = {0.390388203, -0.640388203}