7(x-6)2x=9(x-1)-2

Solution for 7(x-6)2x=9(x-1)-2 equation:

Simplifying
7(x + -6) * 2x = 9(x + -1) + -2

Reorder the terms:
7(-6 + x) * 2x = 9(x + -1) + -2

Reorder the terms for easier multiplication:
7 * 2x(-6 + x) = 9(x + -1) + -2

Multiply 7 * 2
14x(-6 + x) = 9(x + -1) + -2
(-6 * 14x + x * 14x) = 9(x + -1) + -2
(-84x + 14x2) = 9(x + -1) + -2

Reorder the terms:
-84x + 14x2 = 9(-1 + x) + -2
-84x + 14x2 = (-1 * 9 + x * 9) + -2
-84x + 14x2 = (-9 + 9x) + -2

Reorder the terms:
-84x + 14x2 = -9 + -2 + 9x

Combine like terms: -9 + -2 = -11
-84x + 14x2 = -11 + 9x

Solving
-84x + 14x2 = -11 + 9x

Solving for variable 'x'.

Reorder the terms:
11 + -84x + -9x + 14x2 = -11 + 9x + 11 + -9x

Combine like terms: -84x + -9x = -93x
11 + -93x + 14x2 = -11 + 9x + 11 + -9x

Reorder the terms:
11 + -93x + 14x2 = -11 + 11 + 9x + -9x

Combine like terms: -11 + 11 = 0
11 + -93x + 14x2 = 0 + 9x + -9x
11 + -93x + 14x2 = 9x + -9x

Combine like terms: 9x + -9x = 0
11 + -93x + 14x2 = 0

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

Divide each side by '14'.
0.7857142857 + -6.642857143x + x2 = 0

Move the constant term to the right:

Add '-0.7857142857' to each side of the equation.
0.7857142857 + -6.642857143x + -0.7857142857 + x2 = 0 + -0.7857142857

Reorder the terms:
0.7857142857 + -0.7857142857 + -6.642857143x + x2 = 0 + -0.7857142857

Combine like terms: 0.7857142857 + -0.7857142857 = 0.0000000000
0.0000000000 + -6.642857143x + x2 = 0 + -0.7857142857
-6.642857143x + x2 = 0 + -0.7857142857

Combine like terms: 0 + -0.7857142857 = -0.7857142857
-6.642857143x + x2 = -0.7857142857

The x term is -6.642857143x.  Take half its coefficient (-3.321428572).
Square it (11.03188776) and add it to both sides.

Add '11.03188776' to each side of the equation.
-6.642857143x + 11.03188776 + x2 = -0.7857142857 + 11.03188776

Reorder the terms:
11.03188776 + -6.642857143x + x2 = -0.7857142857 + 11.03188776

Combine like terms: -0.7857142857 + 11.03188776 = 10.2461734743
11.03188776 + -6.642857143x + x2 = 10.2461734743

Factor a perfect square on the left side:
(x + -3.321428572)(x + -3.321428572) = 10.2461734743

Calculate the square root of the right side: 3.20096446

Break this problem into two subproblems by setting 
(x + -3.321428572) equal to 3.20096446 and -3.20096446.

Subproblem 1
x + -3.321428572 = 3.20096446

Simplifying
x + -3.321428572 = 3.20096446

Reorder the terms:
-3.321428572 + x = 3.20096446

Solving
-3.321428572 + x = 3.20096446

Solving for variable 'x'.

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

Add '3.321428572' to each side of the equation.
-3.321428572 + 3.321428572 + x = 3.20096446 + 3.321428572

Combine like terms: -3.321428572 + 3.321428572 = 0.000000000
0.000000000 + x = 3.20096446 + 3.321428572
x = 3.20096446 + 3.321428572

Combine like terms: 3.20096446 + 3.321428572 = 6.522393032
x = 6.522393032

Simplifying
x = 6.522393032

Subproblem 2
x + -3.321428572 = -3.20096446

Simplifying
x + -3.321428572 = -3.20096446

Reorder the terms:
-3.321428572 + x = -3.20096446

Solving
-3.321428572 + x = -3.20096446

Solving for variable 'x'.

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

Add '3.321428572' to each side of the equation.
-3.321428572 + 3.321428572 + x = -3.20096446 + 3.321428572

Combine like terms: -3.321428572 + 3.321428572 = 0.000000000
0.000000000 + x = -3.20096446 + 3.321428572
x = -3.20096446 + 3.321428572

Combine like terms: -3.20096446 + 3.321428572 = 0.120464112
x = 0.120464112

Simplifying
x = 0.120464112

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.522393032, 0.120464112}