6x-6=(x-7)7x

Solution for 6x-6=(x-7)7x equation:

Simplifying
6x + -6 = (x + -7) * 7x

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

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

Reorder the terms for easier multiplication:
-6 + 6x = 7x(-7 + x)
-6 + 6x = (-7 * 7x + x * 7x)
-6 + 6x = (-49x + 7x2)

Solving
-6 + 6x = -49x + 7x2

Solving for variable 'x'.

Combine like terms: 6x + 49x = 55x
-6 + 55x + -7x2 = -49x + 7x2 + 49x + -7x2

Reorder the terms:
-6 + 55x + -7x2 = -49x + 49x + 7x2 + -7x2

Combine like terms: -49x + 49x = 0
-6 + 55x + -7x2 = 0 + 7x2 + -7x2
-6 + 55x + -7x2 = 7x2 + -7x2

Combine like terms: 7x2 + -7x2 = 0
-6 + 55x + -7x2 = 0

Begin completing the square.  Divide all terms by
-7 the coefficient of the squared term: 

Divide each side by '-7'.
0.8571428571 + -7.857142857x + x2 = 0

Move the constant term to the right:

Add '-0.8571428571' to each side of the equation.
0.8571428571 + -7.857142857x + -0.8571428571 + x2 = 0 + -0.8571428571

Reorder the terms:
0.8571428571 + -0.8571428571 + -7.857142857x + x2 = 0 + -0.8571428571

Combine like terms: 0.8571428571 + -0.8571428571 = 0.0000000000
0.0000000000 + -7.857142857x + x2 = 0 + -0.8571428571
-7.857142857x + x2 = 0 + -0.8571428571

Combine like terms: 0 + -0.8571428571 = -0.8571428571
-7.857142857x + x2 = -0.8571428571

The x term is -7.857142857x.  Take half its coefficient (-3.928571429).
Square it (15.43367347) and add it to both sides.

Add '15.43367347' to each side of the equation.
-7.857142857x + 15.43367347 + x2 = -0.8571428571 + 15.43367347

Reorder the terms:
15.43367347 + -7.857142857x + x2 = -0.8571428571 + 15.43367347

Combine like terms: -0.8571428571 + 15.43367347 = 14.5765306129
15.43367347 + -7.857142857x + x2 = 14.5765306129

Factor a perfect square on the left side:
(x + -3.928571429)(x + -3.928571429) = 14.5765306129

Calculate the square root of the right side: 3.81792229

Break this problem into two subproblems by setting 
(x + -3.928571429) equal to 3.81792229 and -3.81792229.

Subproblem 1
x + -3.928571429 = 3.81792229

Simplifying
x + -3.928571429 = 3.81792229

Reorder the terms:
-3.928571429 + x = 3.81792229

Solving
-3.928571429 + x = 3.81792229

Solving for variable 'x'.

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

Add '3.928571429' to each side of the equation.
-3.928571429 + 3.928571429 + x = 3.81792229 + 3.928571429

Combine like terms: -3.928571429 + 3.928571429 = 0.000000000
0.000000000 + x = 3.81792229 + 3.928571429
x = 3.81792229 + 3.928571429

Combine like terms: 3.81792229 + 3.928571429 = 7.746493719
x = 7.746493719

Simplifying
x = 7.746493719

Subproblem 2
x + -3.928571429 = -3.81792229

Simplifying
x + -3.928571429 = -3.81792229

Reorder the terms:
-3.928571429 + x = -3.81792229

Solving
-3.928571429 + x = -3.81792229

Solving for variable 'x'.

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

Add '3.928571429' to each side of the equation.
-3.928571429 + 3.928571429 + x = -3.81792229 + 3.928571429

Combine like terms: -3.928571429 + 3.928571429 = 0.000000000
0.000000000 + x = -3.81792229 + 3.928571429
x = -3.81792229 + 3.928571429

Combine like terms: -3.81792229 + 3.928571429 = 0.110649139
x = 0.110649139

Simplifying
x = 0.110649139

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.746493719, 0.110649139}