6(2x-1)x-12=3(7x+6)

Solution for 6(2x-1)x-12=3(7x+6) equation:

Simplifying
6(2x + -1) * x + -12 = 3(7x + 6)

Reorder the terms:
6(-1 + 2x) * x + -12 = 3(7x + 6)

Reorder the terms for easier multiplication:
6x(-1 + 2x) + -12 = 3(7x + 6)
(-1 * 6x + 2x * 6x) + -12 = 3(7x + 6)
(-6x + 12x2) + -12 = 3(7x + 6)

Reorder the terms:
-12 + -6x + 12x2 = 3(7x + 6)

Reorder the terms:
-12 + -6x + 12x2 = 3(6 + 7x)
-12 + -6x + 12x2 = (6 * 3 + 7x * 3)
-12 + -6x + 12x2 = (18 + 21x)

Solving
-12 + -6x + 12x2 = 18 + 21x

Solving for variable 'x'.

Reorder the terms:
-12 + -18 + -6x + -21x + 12x2 = 18 + 21x + -18 + -21x

Combine like terms: -12 + -18 = -30
-30 + -6x + -21x + 12x2 = 18 + 21x + -18 + -21x

Combine like terms: -6x + -21x = -27x
-30 + -27x + 12x2 = 18 + 21x + -18 + -21x

Reorder the terms:
-30 + -27x + 12x2 = 18 + -18 + 21x + -21x

Combine like terms: 18 + -18 = 0
-30 + -27x + 12x2 = 0 + 21x + -21x
-30 + -27x + 12x2 = 21x + -21x

Combine like terms: 21x + -21x = 0
-30 + -27x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-10 + -9x + 4x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-10 + -9x + 4x2)' equal to zero and attempt to solve:

Simplifying
-10 + -9x + 4x2 = 0

Solving
-10 + -9x + 4x2 = 0

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

Divide each side by '4'.
-2.5 + -2.25x + x2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + -2.25x + 2.5 + x2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + -2.25x + x2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + -2.25x + x2 = 0 + 2.5
-2.25x + x2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
-2.25x + x2 = 2.5

The x term is -2.25x.  Take half its coefficient (-1.125).
Square it (1.265625) and add it to both sides.

Add '1.265625' to each side of the equation.
-2.25x + 1.265625 + x2 = 2.5 + 1.265625

Reorder the terms:
1.265625 + -2.25x + x2 = 2.5 + 1.265625

Combine like terms: 2.5 + 1.265625 = 3.765625
1.265625 + -2.25x + x2 = 3.765625

Factor a perfect square on the left side:
(x + -1.125)(x + -1.125) = 3.765625

Calculate the square root of the right side: 1.940521837

Break this problem into two subproblems by setting 
(x + -1.125) equal to 1.940521837 and -1.940521837.

Subproblem 1
x + -1.125 = 1.940521837

Simplifying
x + -1.125 = 1.940521837

Reorder the terms:
-1.125 + x = 1.940521837

Solving
-1.125 + x = 1.940521837

Solving for variable 'x'.

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

Add '1.125' to each side of the equation.
-1.125 + 1.125 + x = 1.940521837 + 1.125

Combine like terms: -1.125 + 1.125 = 0.000
0.000 + x = 1.940521837 + 1.125
x = 1.940521837 + 1.125

Combine like terms: 1.940521837 + 1.125 = 3.065521837
x = 3.065521837

Simplifying
x = 3.065521837

Subproblem 2
x + -1.125 = -1.940521837

Simplifying
x + -1.125 = -1.940521837

Reorder the terms:
-1.125 + x = -1.940521837

Solving
-1.125 + x = -1.940521837

Solving for variable 'x'.

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

Add '1.125' to each side of the equation.
-1.125 + 1.125 + x = -1.940521837 + 1.125

Combine like terms: -1.125 + 1.125 = 0.000
0.000 + x = -1.940521837 + 1.125
x = -1.940521837 + 1.125

Combine like terms: -1.940521837 + 1.125 = -0.815521837
x = -0.815521837

Simplifying
x = -0.815521837

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.065521837, -0.815521837}
Solution
x = {3.065521837, -0.815521837}