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

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

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

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

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

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

Multiply (-7 + 6x) * (6 + 3x)
-1 + 2x = (-7(6 + 3x) + 6x * (6 + 3x))
-1 + 2x = ((6 * -7 + 3x * -7) + 6x * (6 + 3x))
-1 + 2x = ((-42 + -21x) + 6x * (6 + 3x))
-1 + 2x = (-42 + -21x + (6 * 6x + 3x * 6x))
-1 + 2x = (-42 + -21x + (36x + 18x2))

Combine like terms: -21x + 36x = 15x
-1 + 2x = (-42 + 15x + 18x2)

Solving
-1 + 2x = -42 + 15x + 18x2

Solving for variable 'x'.

Reorder the terms:
-1 + 42 + 2x + -15x + -18x2 = -42 + 15x + 18x2 + 42 + -15x + -18x2

Combine like terms: -1 + 42 = 41
41 + 2x + -15x + -18x2 = -42 + 15x + 18x2 + 42 + -15x + -18x2

Combine like terms: 2x + -15x = -13x
41 + -13x + -18x2 = -42 + 15x + 18x2 + 42 + -15x + -18x2

Reorder the terms:
41 + -13x + -18x2 = -42 + 42 + 15x + -15x + 18x2 + -18x2

Combine like terms: -42 + 42 = 0
41 + -13x + -18x2 = 0 + 15x + -15x + 18x2 + -18x2
41 + -13x + -18x2 = 15x + -15x + 18x2 + -18x2

Combine like terms: 15x + -15x = 0
41 + -13x + -18x2 = 0 + 18x2 + -18x2
41 + -13x + -18x2 = 18x2 + -18x2

Combine like terms: 18x2 + -18x2 = 0
41 + -13x + -18x2 = 0

Begin completing the square.  Divide all terms by
-18 the coefficient of the squared term: 

Divide each side by '-18'.
-2.277777778 + 0.7222222222x + x2 = 0

Move the constant term to the right:

Add '2.277777778' to each side of the equation.
-2.277777778 + 0.7222222222x + 2.277777778 + x2 = 0 + 2.277777778

Reorder the terms:
-2.277777778 + 2.277777778 + 0.7222222222x + x2 = 0 + 2.277777778

Combine like terms: -2.277777778 + 2.277777778 = 0.000000000
0.000000000 + 0.7222222222x + x2 = 0 + 2.277777778
0.7222222222x + x2 = 0 + 2.277777778

Combine like terms: 0 + 2.277777778 = 2.277777778
0.7222222222x + x2 = 2.277777778

The x term is 0.7222222222x.  Take half its coefficient (0.3611111111).
Square it (0.1304012346) and add it to both sides.

Add '0.1304012346' to each side of the equation.
0.7222222222x + 0.1304012346 + x2 = 2.277777778 + 0.1304012346

Reorder the terms:
0.1304012346 + 0.7222222222x + x2 = 2.277777778 + 0.1304012346

Combine like terms: 2.277777778 + 0.1304012346 = 2.4081790126
0.1304012346 + 0.7222222222x + x2 = 2.4081790126

Factor a perfect square on the left side:
(x + 0.3611111111)(x + 0.3611111111) = 2.4081790126

Calculate the square root of the right side: 1.551830858

Break this problem into two subproblems by setting 
(x + 0.3611111111) equal to 1.551830858 and -1.551830858.

Subproblem 1
x + 0.3611111111 = 1.551830858

Simplifying
x + 0.3611111111 = 1.551830858

Reorder the terms:
0.3611111111 + x = 1.551830858

Solving
0.3611111111 + x = 1.551830858

Solving for variable 'x'.

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

Add '-0.3611111111' to each side of the equation.
0.3611111111 + -0.3611111111 + x = 1.551830858 + -0.3611111111

Combine like terms: 0.3611111111 + -0.3611111111 = 0.0000000000
0.0000000000 + x = 1.551830858 + -0.3611111111
x = 1.551830858 + -0.3611111111

Combine like terms: 1.551830858 + -0.3611111111 = 1.1907197469
x = 1.1907197469

Simplifying
x = 1.1907197469

Subproblem 2
x + 0.3611111111 = -1.551830858

Simplifying
x + 0.3611111111 = -1.551830858

Reorder the terms:
0.3611111111 + x = -1.551830858

Solving
0.3611111111 + x = -1.551830858

Solving for variable 'x'.

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

Add '-0.3611111111' to each side of the equation.
0.3611111111 + -0.3611111111 + x = -1.551830858 + -0.3611111111

Combine like terms: 0.3611111111 + -0.3611111111 = 0.0000000000
0.0000000000 + x = -1.551830858 + -0.3611111111
x = -1.551830858 + -0.3611111111

Combine like terms: -1.551830858 + -0.3611111111 = -1.9129419691
x = -1.9129419691

Simplifying
x = -1.9129419691

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.1907197469, -1.9129419691}