6[-6x+6+4](x+1)=6x+2

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

Simplifying
6[-6x + 6 + 4](x + 1) = 6x + 2

Reorder the terms:
6[6 + 4 + -6x](x + 1) = 6x + 2

Combine like terms: 6 + 4 = 10
6[10 + -6x](x + 1) = 6x + 2

Reorder the terms:
6[10 + -6x](1 + x) = 6x + 2

Multiply [10 + -6x] * (1 + x)
6[10(1 + x) + -6x * (1 + x)] = 6x + 2
6[(1 * 10 + x * 10) + -6x * (1 + x)] = 6x + 2
6[(10 + 10x) + -6x * (1 + x)] = 6x + 2
6[10 + 10x + (1 * -6x + x * -6x)] = 6x + 2
6[10 + 10x + (-6x + -6x2)] = 6x + 2

Combine like terms: 10x + -6x = 4x
6[10 + 4x + -6x2] = 6x + 2
[10 * 6 + 4x * 6 + -6x2 * 6] = 6x + 2
[60 + 24x + -36x2] = 6x + 2

Reorder the terms:
60 + 24x + -36x2 = 2 + 6x

Solving
60 + 24x + -36x2 = 2 + 6x

Solving for variable 'x'.

Reorder the terms:
60 + -2 + 24x + -6x + -36x2 = 2 + 6x + -2 + -6x

Combine like terms: 60 + -2 = 58
58 + 24x + -6x + -36x2 = 2 + 6x + -2 + -6x

Combine like terms: 24x + -6x = 18x
58 + 18x + -36x2 = 2 + 6x + -2 + -6x

Reorder the terms:
58 + 18x + -36x2 = 2 + -2 + 6x + -6x

Combine like terms: 2 + -2 = 0
58 + 18x + -36x2 = 0 + 6x + -6x
58 + 18x + -36x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
58 + 18x + -36x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(29 + 9x + -18x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(29 + 9x + -18x2)' equal to zero and attempt to solve:

Simplifying
29 + 9x + -18x2 = 0

Solving
29 + 9x + -18x2 = 0

Begin completing the square.  Divide all terms by
-18 the coefficient of the squared term: 

Divide each side by '-18'.
-1.611111111 + -0.5x + x2 = 0

Move the constant term to the right:

Add '1.611111111' to each side of the equation.
-1.611111111 + -0.5x + 1.611111111 + x2 = 0 + 1.611111111

Reorder the terms:
-1.611111111 + 1.611111111 + -0.5x + x2 = 0 + 1.611111111

Combine like terms: -1.611111111 + 1.611111111 = 0.000000000
0.000000000 + -0.5x + x2 = 0 + 1.611111111
-0.5x + x2 = 0 + 1.611111111

Combine like terms: 0 + 1.611111111 = 1.611111111
-0.5x + x2 = 1.611111111

The x term is -0.5x.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5x + 0.0625 + x2 = 1.611111111 + 0.0625

Reorder the terms:
0.0625 + -0.5x + x2 = 1.611111111 + 0.0625

Combine like terms: 1.611111111 + 0.0625 = 1.673611111
0.0625 + -0.5x + x2 = 1.673611111

Factor a perfect square on the left side:
(x + -0.25)(x + -0.25) = 1.673611111

Calculate the square root of the right side: 1.293681225

Break this problem into two subproblems by setting 
(x + -0.25) equal to 1.293681225 and -1.293681225.

Subproblem 1
x + -0.25 = 1.293681225

Simplifying
x + -0.25 = 1.293681225

Reorder the terms:
-0.25 + x = 1.293681225

Solving
-0.25 + x = 1.293681225

Solving for variable 'x'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + x = 1.293681225 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + x = 1.293681225 + 0.25
x = 1.293681225 + 0.25

Combine like terms: 1.293681225 + 0.25 = 1.543681225
x = 1.543681225

Simplifying
x = 1.543681225

Subproblem 2
x + -0.25 = -1.293681225

Simplifying
x + -0.25 = -1.293681225

Reorder the terms:
-0.25 + x = -1.293681225

Solving
-0.25 + x = -1.293681225

Solving for variable 'x'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + x = -1.293681225 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + x = -1.293681225 + 0.25
x = -1.293681225 + 0.25

Combine like terms: -1.293681225 + 0.25 = -1.043681225
x = -1.043681225

Simplifying
x = -1.043681225

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.543681225, -1.043681225}
Solution
x = {1.543681225, -1.043681225}