(6x-1)(2x+3)=9x

Solution for (6x-1)(2x+3)=9x equation:

Simplifying
(6x + -1)(2x + 3) = 9x

Reorder the terms:
(-1 + 6x)(2x + 3) = 9x

Reorder the terms:
(-1 + 6x)(3 + 2x) = 9x

Multiply (-1 + 6x) * (3 + 2x)
(-1(3 + 2x) + 6x * (3 + 2x)) = 9x
((3 * -1 + 2x * -1) + 6x * (3 + 2x)) = 9x
((-3 + -2x) + 6x * (3 + 2x)) = 9x
(-3 + -2x + (3 * 6x + 2x * 6x)) = 9x
(-3 + -2x + (18x + 12x2)) = 9x

Combine like terms: -2x + 18x = 16x
(-3 + 16x + 12x2) = 9x

Solving
-3 + 16x + 12x2 = 9x

Solving for variable 'x'.

Reorder the terms:
-3 + 16x + -9x + 12x2 = 9x + -9x

Combine like terms: 16x + -9x = 7x
-3 + 7x + 12x2 = 9x + -9x

Combine like terms: 9x + -9x = 0
-3 + 7x + 12x2 = 0

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

Divide each side by '12'.
-0.25 + 0.5833333333x + x2 = 0

Move the constant term to the right:

Add '0.25' to each side of the equation.
-0.25 + 0.5833333333x + 0.25 + x2 = 0 + 0.25

Reorder the terms:
-0.25 + 0.25 + 0.5833333333x + x2 = 0 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + 0.5833333333x + x2 = 0 + 0.25
0.5833333333x + x2 = 0 + 0.25

Combine like terms: 0 + 0.25 = 0.25
0.5833333333x + x2 = 0.25

The x term is 0.5833333333x.  Take half its coefficient (0.2916666667).
Square it (0.08506944446) and add it to both sides.

Add '0.08506944446' to each side of the equation.
0.5833333333x + 0.08506944446 + x2 = 0.25 + 0.08506944446

Reorder the terms:
0.08506944446 + 0.5833333333x + x2 = 0.25 + 0.08506944446

Combine like terms: 0.25 + 0.08506944446 = 0.33506944446
0.08506944446 + 0.5833333333x + x2 = 0.33506944446

Factor a perfect square on the left side:
(x + 0.2916666667)(x + 0.2916666667) = 0.33506944446

Calculate the square root of the right side: 0.578851833

Break this problem into two subproblems by setting 
(x + 0.2916666667) equal to 0.578851833 and -0.578851833.

Subproblem 1
x + 0.2916666667 = 0.578851833

Simplifying
x + 0.2916666667 = 0.578851833

Reorder the terms:
0.2916666667 + x = 0.578851833

Solving
0.2916666667 + x = 0.578851833

Solving for variable 'x'.

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

Add '-0.2916666667' to each side of the equation.
0.2916666667 + -0.2916666667 + x = 0.578851833 + -0.2916666667

Combine like terms: 0.2916666667 + -0.2916666667 = 0.0000000000
0.0000000000 + x = 0.578851833 + -0.2916666667
x = 0.578851833 + -0.2916666667

Combine like terms: 0.578851833 + -0.2916666667 = 0.2871851663
x = 0.2871851663

Simplifying
x = 0.2871851663

Subproblem 2
x + 0.2916666667 = -0.578851833

Simplifying
x + 0.2916666667 = -0.578851833

Reorder the terms:
0.2916666667 + x = -0.578851833

Solving
0.2916666667 + x = -0.578851833

Solving for variable 'x'.

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

Add '-0.2916666667' to each side of the equation.
0.2916666667 + -0.2916666667 + x = -0.578851833 + -0.2916666667

Combine like terms: 0.2916666667 + -0.2916666667 = 0.0000000000
0.0000000000 + x = -0.578851833 + -0.2916666667
x = -0.578851833 + -0.2916666667

Combine like terms: -0.578851833 + -0.2916666667 = -0.8705184997
x = -0.8705184997

Simplifying
x = -0.8705184997

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.2871851663, -0.8705184997}