(6x-18)(3x+2)=2

Solution for (6x-18)(3x+2)=2 equation:

Simplifying
(6x + -18)(3x + 2) = 2

Reorder the terms:
(-18 + 6x)(3x + 2) = 2

Reorder the terms:
(-18 + 6x)(2 + 3x) = 2

Multiply (-18 + 6x) * (2 + 3x)
(-18(2 + 3x) + 6x * (2 + 3x)) = 2
((2 * -18 + 3x * -18) + 6x * (2 + 3x)) = 2
((-36 + -54x) + 6x * (2 + 3x)) = 2
(-36 + -54x + (2 * 6x + 3x * 6x)) = 2
(-36 + -54x + (12x + 18x2)) = 2

Combine like terms: -54x + 12x = -42x
(-36 + -42x + 18x2) = 2

Solving
-36 + -42x + 18x2 = 2

Solving for variable 'x'.

Reorder the terms:
-36 + -2 + -42x + 18x2 = 2 + -2

Combine like terms: -36 + -2 = -38
-38 + -42x + 18x2 = 2 + -2

Combine like terms: 2 + -2 = 0
-38 + -42x + 18x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-19 + -21x + 9x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-19 + -21x + 9x2)' equal to zero and attempt to solve:

Simplifying
-19 + -21x + 9x2 = 0

Solving
-19 + -21x + 9x2 = 0

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

Divide each side by '9'.
-2.111111111 + -2.333333333x + x2 = 0

Move the constant term to the right:

Add '2.111111111' to each side of the equation.
-2.111111111 + -2.333333333x + 2.111111111 + x2 = 0 + 2.111111111

Reorder the terms:
-2.111111111 + 2.111111111 + -2.333333333x + x2 = 0 + 2.111111111

Combine like terms: -2.111111111 + 2.111111111 = 0.000000000
0.000000000 + -2.333333333x + x2 = 0 + 2.111111111
-2.333333333x + x2 = 0 + 2.111111111

Combine like terms: 0 + 2.111111111 = 2.111111111
-2.333333333x + x2 = 2.111111111

The x term is -2.333333333x.  Take half its coefficient (-1.166666667).
Square it (1.361111112) and add it to both sides.

Add '1.361111112' to each side of the equation.
-2.333333333x + 1.361111112 + x2 = 2.111111111 + 1.361111112

Reorder the terms:
1.361111112 + -2.333333333x + x2 = 2.111111111 + 1.361111112

Combine like terms: 2.111111111 + 1.361111112 = 3.472222223
1.361111112 + -2.333333333x + x2 = 3.472222223

Factor a perfect square on the left side:
(x + -1.166666667)(x + -1.166666667) = 3.472222223

Calculate the square root of the right side: 1.863389981

Break this problem into two subproblems by setting 
(x + -1.166666667) equal to 1.863389981 and -1.863389981.

Subproblem 1
x + -1.166666667 = 1.863389981

Simplifying
x + -1.166666667 = 1.863389981

Reorder the terms:
-1.166666667 + x = 1.863389981

Solving
-1.166666667 + x = 1.863389981

Solving for variable 'x'.

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

Add '1.166666667' to each side of the equation.
-1.166666667 + 1.166666667 + x = 1.863389981 + 1.166666667

Combine like terms: -1.166666667 + 1.166666667 = 0.000000000
0.000000000 + x = 1.863389981 + 1.166666667
x = 1.863389981 + 1.166666667

Combine like terms: 1.863389981 + 1.166666667 = 3.030056648
x = 3.030056648

Simplifying
x = 3.030056648

Subproblem 2
x + -1.166666667 = -1.863389981

Simplifying
x + -1.166666667 = -1.863389981

Reorder the terms:
-1.166666667 + x = -1.863389981

Solving
-1.166666667 + x = -1.863389981

Solving for variable 'x'.

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

Add '1.166666667' to each side of the equation.
-1.166666667 + 1.166666667 + x = -1.863389981 + 1.166666667

Combine like terms: -1.166666667 + 1.166666667 = 0.000000000
0.000000000 + x = -1.863389981 + 1.166666667
x = -1.863389981 + 1.166666667

Combine like terms: -1.863389981 + 1.166666667 = -0.696723314
x = -0.696723314

Simplifying
x = -0.696723314

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.030056648, -0.696723314}
Solution
x = {3.030056648, -0.696723314}