12x(x-6)+8x=7(3x+2)-8

Solution for 12x(x-6)+8x=7(3x+2)-8 equation:

Simplifying
12x(x + -6) + 8x = 7(3x + 2) + -8

Reorder the terms:
12x(-6 + x) + 8x = 7(3x + 2) + -8
(-6 * 12x + x * 12x) + 8x = 7(3x + 2) + -8
(-72x + 12x2) + 8x = 7(3x + 2) + -8

Reorder the terms:
-72x + 8x + 12x2 = 7(3x + 2) + -8

Combine like terms: -72x + 8x = -64x
-64x + 12x2 = 7(3x + 2) + -8

Reorder the terms:
-64x + 12x2 = 7(2 + 3x) + -8
-64x + 12x2 = (2 * 7 + 3x * 7) + -8
-64x + 12x2 = (14 + 21x) + -8

Reorder the terms:
-64x + 12x2 = 14 + -8 + 21x

Combine like terms: 14 + -8 = 6
-64x + 12x2 = 6 + 21x

Solving
-64x + 12x2 = 6 + 21x

Solving for variable 'x'.

Reorder the terms:
-6 + -64x + -21x + 12x2 = 6 + 21x + -6 + -21x

Combine like terms: -64x + -21x = -85x
-6 + -85x + 12x2 = 6 + 21x + -6 + -21x

Reorder the terms:
-6 + -85x + 12x2 = 6 + -6 + 21x + -21x

Combine like terms: 6 + -6 = 0
-6 + -85x + 12x2 = 0 + 21x + -21x
-6 + -85x + 12x2 = 21x + -21x

Combine like terms: 21x + -21x = 0
-6 + -85x + 12x2 = 0

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

Divide each side by '12'.
-0.5 + -7.083333333x + x2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + -7.083333333x + 0.5 + x2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + -7.083333333x + x2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + -7.083333333x + x2 = 0 + 0.5
-7.083333333x + x2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
-7.083333333x + x2 = 0.5

The x term is -7.083333333x.  Take half its coefficient (-3.541666667).
Square it (12.54340278) and add it to both sides.

Add '12.54340278' to each side of the equation.
-7.083333333x + 12.54340278 + x2 = 0.5 + 12.54340278

Reorder the terms:
12.54340278 + -7.083333333x + x2 = 0.5 + 12.54340278

Combine like terms: 0.5 + 12.54340278 = 13.04340278
12.54340278 + -7.083333333x + x2 = 13.04340278

Factor a perfect square on the left side:
(x + -3.541666667)(x + -3.541666667) = 13.04340278

Calculate the square root of the right side: 3.611565143

Break this problem into two subproblems by setting 
(x + -3.541666667) equal to 3.611565143 and -3.611565143.

Subproblem 1
x + -3.541666667 = 3.611565143

Simplifying
x + -3.541666667 = 3.611565143

Reorder the terms:
-3.541666667 + x = 3.611565143

Solving
-3.541666667 + x = 3.611565143

Solving for variable 'x'.

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

Add '3.541666667' to each side of the equation.
-3.541666667 + 3.541666667 + x = 3.611565143 + 3.541666667

Combine like terms: -3.541666667 + 3.541666667 = 0.000000000
0.000000000 + x = 3.611565143 + 3.541666667
x = 3.611565143 + 3.541666667

Combine like terms: 3.611565143 + 3.541666667 = 7.15323181
x = 7.15323181

Simplifying
x = 7.15323181

Subproblem 2
x + -3.541666667 = -3.611565143

Simplifying
x + -3.541666667 = -3.611565143

Reorder the terms:
-3.541666667 + x = -3.611565143

Solving
-3.541666667 + x = -3.611565143

Solving for variable 'x'.

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

Add '3.541666667' to each side of the equation.
-3.541666667 + 3.541666667 + x = -3.611565143 + 3.541666667

Combine like terms: -3.541666667 + 3.541666667 = 0.000000000
0.000000000 + x = -3.611565143 + 3.541666667
x = -3.611565143 + 3.541666667

Combine like terms: -3.611565143 + 3.541666667 = -0.069898476
x = -0.069898476

Simplifying
x = -0.069898476

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.15323181, -0.069898476}