(9x+7)(6x+8)=180

Solution for (9x+7)(6x+8)=180 equation:

Simplifying
(9x + 7)(6x + 8) = 180

Reorder the terms:
(7 + 9x)(6x + 8) = 180

Reorder the terms:
(7 + 9x)(8 + 6x) = 180

Multiply (7 + 9x) * (8 + 6x)
(7(8 + 6x) + 9x * (8 + 6x)) = 180
((8 * 7 + 6x * 7) + 9x * (8 + 6x)) = 180
((56 + 42x) + 9x * (8 + 6x)) = 180
(56 + 42x + (8 * 9x + 6x * 9x)) = 180
(56 + 42x + (72x + 54x2)) = 180

Combine like terms: 42x + 72x = 114x
(56 + 114x + 54x2) = 180

Solving
56 + 114x + 54x2 = 180

Solving for variable 'x'.

Reorder the terms:
56 + -180 + 114x + 54x2 = 180 + -180

Combine like terms: 56 + -180 = -124
-124 + 114x + 54x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-124 + 114x + 54x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-62 + 57x + 27x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-62 + 57x + 27x2)' equal to zero and attempt to solve:

Simplifying
-62 + 57x + 27x2 = 0

Solving
-62 + 57x + 27x2 = 0

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

Divide each side by '27'.
-2.296296296 + 2.111111111x + x2 = 0

Move the constant term to the right:

Add '2.296296296' to each side of the equation.
-2.296296296 + 2.111111111x + 2.296296296 + x2 = 0 + 2.296296296

Reorder the terms:
-2.296296296 + 2.296296296 + 2.111111111x + x2 = 0 + 2.296296296

Combine like terms: -2.296296296 + 2.296296296 = 0.000000000
0.000000000 + 2.111111111x + x2 = 0 + 2.296296296
2.111111111x + x2 = 0 + 2.296296296

Combine like terms: 0 + 2.296296296 = 2.296296296
2.111111111x + x2 = 2.296296296

The x term is 2.111111111x.  Take half its coefficient (1.055555556).
Square it (1.114197532) and add it to both sides.

Add '1.114197532' to each side of the equation.
2.111111111x + 1.114197532 + x2 = 2.296296296 + 1.114197532

Reorder the terms:
1.114197532 + 2.111111111x + x2 = 2.296296296 + 1.114197532

Combine like terms: 2.296296296 + 1.114197532 = 3.410493828
1.114197532 + 2.111111111x + x2 = 3.410493828

Factor a perfect square on the left side:
(x + 1.055555556)(x + 1.055555556) = 3.410493828

Calculate the square root of the right side: 1.846752238

Break this problem into two subproblems by setting 
(x + 1.055555556) equal to 1.846752238 and -1.846752238.

Subproblem 1
x + 1.055555556 = 1.846752238

Simplifying
x + 1.055555556 = 1.846752238

Reorder the terms:
1.055555556 + x = 1.846752238

Solving
1.055555556 + x = 1.846752238

Solving for variable 'x'.

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

Add '-1.055555556' to each side of the equation.
1.055555556 + -1.055555556 + x = 1.846752238 + -1.055555556

Combine like terms: 1.055555556 + -1.055555556 = 0.000000000
0.000000000 + x = 1.846752238 + -1.055555556
x = 1.846752238 + -1.055555556

Combine like terms: 1.846752238 + -1.055555556 = 0.791196682
x = 0.791196682

Simplifying
x = 0.791196682

Subproblem 2
x + 1.055555556 = -1.846752238

Simplifying
x + 1.055555556 = -1.846752238

Reorder the terms:
1.055555556 + x = -1.846752238

Solving
1.055555556 + x = -1.846752238

Solving for variable 'x'.

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

Add '-1.055555556' to each side of the equation.
1.055555556 + -1.055555556 + x = -1.846752238 + -1.055555556

Combine like terms: 1.055555556 + -1.055555556 = 0.000000000
0.000000000 + x = -1.846752238 + -1.055555556
x = -1.846752238 + -1.055555556

Combine like terms: -1.846752238 + -1.055555556 = -2.902307794
x = -2.902307794

Simplifying
x = -2.902307794

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.791196682, -2.902307794}
Solution
x = {0.791196682, -2.902307794}