6-5x(0.12x-3)=.13x-7+(2x-0.1x)

Solution for 6-5x(0.12x-3)=.13x-7+(2x-0.1x) equation:

Simplifying
6 + -5x(0.12x + -3) = 0.13x + -7 + (2x + -0.1x)

Reorder the terms:
6 + -5x(-3 + 0.12x) = 0.13x + -7 + (2x + -0.1x)
6 + (-3 * -5x + 0.12x * -5x) = 0.13x + -7 + (2x + -0.1x)
6 + (15x + -0.6x2) = 0.13x + -7 + (2x + -0.1x)

Combine like terms: 2x + -0.1x = 1.9x
6 + 15x + -0.6x2 = 0.13x + -7 + (1.9x)
6 + 15x + -0.6x2 = 0.13x + -7 + (1.9x)

Reorder the terms:
6 + 15x + -0.6x2 = -7 + 0.13x + (1.9x)

Combine like terms: 0.13x + (1.9x) = 2.03x
6 + 15x + -0.6x2 = -7 + 2.03x

Solving
6 + 15x + -0.6x2 = -7 + 2.03x

Solving for variable 'x'.

Reorder the terms:
6 + 7 + 15x + -2.03x + -0.6x2 = -7 + 2.03x + 7 + -2.03x

Combine like terms: 6 + 7 = 13
13 + 15x + -2.03x + -0.6x2 = -7 + 2.03x + 7 + -2.03x

Combine like terms: 15x + -2.03x = 12.97x
13 + 12.97x + -0.6x2 = -7 + 2.03x + 7 + -2.03x

Reorder the terms:
13 + 12.97x + -0.6x2 = -7 + 7 + 2.03x + -2.03x

Combine like terms: -7 + 7 = 0
13 + 12.97x + -0.6x2 = 0 + 2.03x + -2.03x
13 + 12.97x + -0.6x2 = 2.03x + -2.03x

Combine like terms: 2.03x + -2.03x = 0.00
13 + 12.97x + -0.6x2 = 0.00

Begin completing the square.  Divide all terms by
-0.6 the coefficient of the squared term: 

Divide each side by '-0.6'.
-21.66666667 + -21.61666667x + x2 = 0.0

Move the constant term to the right:

Add '21.66666667' to each side of the equation.
-21.66666667 + -21.61666667x + 21.66666667 + x2 = 0.0 + 21.66666667

Reorder the terms:
-21.66666667 + 21.66666667 + -21.61666667x + x2 = 0.0 + 21.66666667

Combine like terms: -21.66666667 + 21.66666667 = 0.00000000
0.00000000 + -21.61666667x + x2 = 0.0 + 21.66666667
-21.61666667x + x2 = 0.0 + 21.66666667

Combine like terms: 0.0 + 21.66666667 = 21.66666667
-21.61666667x + x2 = 21.66666667

The x term is -21.61666667x.  Take half its coefficient (-10.80833334).
Square it (116.8200696) and add it to both sides.

Add '116.8200696' to each side of the equation.
-21.61666667x + 116.8200696 + x2 = 21.66666667 + 116.8200696

Reorder the terms:
116.8200696 + -21.61666667x + x2 = 21.66666667 + 116.8200696

Combine like terms: 21.66666667 + 116.8200696 = 138.48673627
116.8200696 + -21.61666667x + x2 = 138.48673627

Factor a perfect square on the left side:
(x + -10.80833334)(x + -10.80833334) = 138.48673627

Calculate the square root of the right side: 11.768038761

Break this problem into two subproblems by setting 
(x + -10.80833334) equal to 11.768038761 and -11.768038761.

Subproblem 1
x + -10.80833334 = 11.768038761

Simplifying
x + -10.80833334 = 11.768038761

Reorder the terms:
-10.80833334 + x = 11.768038761

Solving
-10.80833334 + x = 11.768038761

Solving for variable 'x'.

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

Add '10.80833334' to each side of the equation.
-10.80833334 + 10.80833334 + x = 11.768038761 + 10.80833334

Combine like terms: -10.80833334 + 10.80833334 = 0.00000000
0.00000000 + x = 11.768038761 + 10.80833334
x = 11.768038761 + 10.80833334

Combine like terms: 11.768038761 + 10.80833334 = 22.576372101
x = 22.576372101

Simplifying
x = 22.576372101

Subproblem 2
x + -10.80833334 = -11.768038761

Simplifying
x + -10.80833334 = -11.768038761

Reorder the terms:
-10.80833334 + x = -11.768038761

Solving
-10.80833334 + x = -11.768038761

Solving for variable 'x'.

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

Add '10.80833334' to each side of the equation.
-10.80833334 + 10.80833334 + x = -11.768038761 + 10.80833334

Combine like terms: -10.80833334 + 10.80833334 = 0.00000000
0.00000000 + x = -11.768038761 + 10.80833334
x = -11.768038761 + 10.80833334

Combine like terms: -11.768038761 + 10.80833334 = -0.959705421
x = -0.959705421

Simplifying
x = -0.959705421

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {22.576372101, -0.959705421}