7a(a-2)-6=2a+8+a

Solution for 7a(a-2)-6=2a+8+a equation:

Simplifying
7a(a + -2) + -6 = 2a + 8 + a

Reorder the terms:
7a(-2 + a) + -6 = 2a + 8 + a
(-2 * 7a + a * 7a) + -6 = 2a + 8 + a
(-14a + 7a2) + -6 = 2a + 8 + a

Reorder the terms:
-6 + -14a + 7a2 = 2a + 8 + a

Reorder the terms:
-6 + -14a + 7a2 = 8 + 2a + a

Combine like terms: 2a + a = 3a
-6 + -14a + 7a2 = 8 + 3a

Solving
-6 + -14a + 7a2 = 8 + 3a

Solving for variable 'a'.

Reorder the terms:
-6 + -8 + -14a + -3a + 7a2 = 8 + 3a + -8 + -3a

Combine like terms: -6 + -8 = -14
-14 + -14a + -3a + 7a2 = 8 + 3a + -8 + -3a

Combine like terms: -14a + -3a = -17a
-14 + -17a + 7a2 = 8 + 3a + -8 + -3a

Reorder the terms:
-14 + -17a + 7a2 = 8 + -8 + 3a + -3a

Combine like terms: 8 + -8 = 0
-14 + -17a + 7a2 = 0 + 3a + -3a
-14 + -17a + 7a2 = 3a + -3a

Combine like terms: 3a + -3a = 0
-14 + -17a + 7a2 = 0

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

Divide each side by '7'.
-2 + -2.428571429a + a2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -2.428571429a + 2 + a2 = 0 + 2

Reorder the terms:
-2 + 2 + -2.428571429a + a2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -2.428571429a + a2 = 0 + 2
-2.428571429a + a2 = 0 + 2

Combine like terms: 0 + 2 = 2
-2.428571429a + a2 = 2

The a term is -2.428571429a.  Take half its coefficient (-1.214285715).
Square it (1.474489798) and add it to both sides.

Add '1.474489798' to each side of the equation.
-2.428571429a + 1.474489798 + a2 = 2 + 1.474489798

Reorder the terms:
1.474489798 + -2.428571429a + a2 = 2 + 1.474489798

Combine like terms: 2 + 1.474489798 = 3.474489798
1.474489798 + -2.428571429a + a2 = 3.474489798

Factor a perfect square on the left side:
(a + -1.214285715)(a + -1.214285715) = 3.474489798

Calculate the square root of the right side: 1.863998336

Break this problem into two subproblems by setting 
(a + -1.214285715) equal to 1.863998336 and -1.863998336.

Subproblem 1
a + -1.214285715 = 1.863998336

Simplifying
a + -1.214285715 = 1.863998336

Reorder the terms:
-1.214285715 + a = 1.863998336

Solving
-1.214285715 + a = 1.863998336

Solving for variable 'a'.

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

Add '1.214285715' to each side of the equation.
-1.214285715 + 1.214285715 + a = 1.863998336 + 1.214285715

Combine like terms: -1.214285715 + 1.214285715 = 0.000000000
0.000000000 + a = 1.863998336 + 1.214285715
a = 1.863998336 + 1.214285715

Combine like terms: 1.863998336 + 1.214285715 = 3.078284051
a = 3.078284051

Simplifying
a = 3.078284051

Subproblem 2
a + -1.214285715 = -1.863998336

Simplifying
a + -1.214285715 = -1.863998336

Reorder the terms:
-1.214285715 + a = -1.863998336

Solving
-1.214285715 + a = -1.863998336

Solving for variable 'a'.

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

Add '1.214285715' to each side of the equation.
-1.214285715 + 1.214285715 + a = -1.863998336 + 1.214285715

Combine like terms: -1.214285715 + 1.214285715 = 0.000000000
0.000000000 + a = -1.863998336 + 1.214285715
a = -1.863998336 + 1.214285715

Combine like terms: -1.863998336 + 1.214285715 = -0.649712621
a = -0.649712621

Simplifying
a = -0.649712621

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {3.078284051, -0.649712621}