0.7(6x+2)=1.1-(x+6)2x

Solution for 0.7(6x+2)=1.1-(x+6)2x equation:

Simplifying
0.7(6x + 2) = 1.1 + -1(x + 6) * 2x

Reorder the terms:
0.7(2 + 6x) = 1.1 + -1(x + 6) * 2x
(2 * 0.7 + 6x * 0.7) = 1.1 + -1(x + 6) * 2x
(1.4 + 4.2x) = 1.1 + -1(x + 6) * 2x

Reorder the terms:
1.4 + 4.2x = 1.1 + -1(6 + x) * 2x

Reorder the terms for easier multiplication:
1.4 + 4.2x = 1.1 + -1 * 2x(6 + x)

Multiply -1 * 2
1.4 + 4.2x = 1.1 + -2x(6 + x)
1.4 + 4.2x = 1.1 + (6 * -2x + x * -2x)
1.4 + 4.2x = 1.1 + (-12x + -2x2)

Solving
1.4 + 4.2x = 1.1 + -12x + -2x2

Solving for variable 'x'.

Reorder the terms:
1.4 + -1.1 + 4.2x + 12x + 2x2 = 1.1 + -12x + -2x2 + -1.1 + 12x + 2x2

Combine like terms: 1.4 + -1.1 = 0.3
0.3 + 4.2x + 12x + 2x2 = 1.1 + -12x + -2x2 + -1.1 + 12x + 2x2

Combine like terms: 4.2x + 12x = 16.2x
0.3 + 16.2x + 2x2 = 1.1 + -12x + -2x2 + -1.1 + 12x + 2x2

Reorder the terms:
0.3 + 16.2x + 2x2 = 1.1 + -1.1 + -12x + 12x + -2x2 + 2x2

Combine like terms: 1.1 + -1.1 = 0.0
0.3 + 16.2x + 2x2 = 0.0 + -12x + 12x + -2x2 + 2x2
0.3 + 16.2x + 2x2 = -12x + 12x + -2x2 + 2x2

Combine like terms: -12x + 12x = 0
0.3 + 16.2x + 2x2 = 0 + -2x2 + 2x2
0.3 + 16.2x + 2x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
0.3 + 16.2x + 2x2 = 0

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

Divide each side by '2'.
0.15 + 8.1x + x2 = 0

Move the constant term to the right:

Add '-0.15' to each side of the equation.
0.15 + 8.1x + -0.15 + x2 = 0 + -0.15

Reorder the terms:
0.15 + -0.15 + 8.1x + x2 = 0 + -0.15

Combine like terms: 0.15 + -0.15 = 0.00
0.00 + 8.1x + x2 = 0 + -0.15
8.1x + x2 = 0 + -0.15

Combine like terms: 0 + -0.15 = -0.15
8.1x + x2 = -0.15

The x term is 8.1x.  Take half its coefficient (4.05).
Square it (16.4025) and add it to both sides.

Add '16.4025' to each side of the equation.
8.1x + 16.4025 + x2 = -0.15 + 16.4025

Reorder the terms:
16.4025 + 8.1x + x2 = -0.15 + 16.4025

Combine like terms: -0.15 + 16.4025 = 16.2525
16.4025 + 8.1x + x2 = 16.2525

Factor a perfect square on the left side:
(x + 4.05)(x + 4.05) = 16.2525

Calculate the square root of the right side: 4.031438949

Break this problem into two subproblems by setting 
(x + 4.05) equal to 4.031438949 and -4.031438949.

Subproblem 1
x + 4.05 = 4.031438949

Simplifying
x + 4.05 = 4.031438949

Reorder the terms:
4.05 + x = 4.031438949

Solving
4.05 + x = 4.031438949

Solving for variable 'x'.

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

Add '-4.05' to each side of the equation.
4.05 + -4.05 + x = 4.031438949 + -4.05

Combine like terms: 4.05 + -4.05 = 0.00
0.00 + x = 4.031438949 + -4.05
x = 4.031438949 + -4.05

Combine like terms: 4.031438949 + -4.05 = -0.018561051
x = -0.018561051

Simplifying
x = -0.018561051

Subproblem 2
x + 4.05 = -4.031438949

Simplifying
x + 4.05 = -4.031438949

Reorder the terms:
4.05 + x = -4.031438949

Solving
4.05 + x = -4.031438949

Solving for variable 'x'.

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

Add '-4.05' to each side of the equation.
4.05 + -4.05 + x = -4.031438949 + -4.05

Combine like terms: 4.05 + -4.05 = 0.00
0.00 + x = -4.031438949 + -4.05
x = -4.031438949 + -4.05

Combine like terms: -4.031438949 + -4.05 = -8.081438949
x = -8.081438949

Simplifying
x = -8.081438949

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.018561051, -8.081438949}