(8x+-19)(9x+-9)=180

Solution for (8x+-19)(9x+-9)=180 equation:

Simplifying
(8x + -19)(9x + -9) = 180

Reorder the terms:
(-19 + 8x)(9x + -9) = 180

Reorder the terms:
(-19 + 8x)(-9 + 9x) = 180

Multiply (-19 + 8x) * (-9 + 9x)
(-19(-9 + 9x) + 8x * (-9 + 9x)) = 180
((-9 * -19 + 9x * -19) + 8x * (-9 + 9x)) = 180
((171 + -171x) + 8x * (-9 + 9x)) = 180
(171 + -171x + (-9 * 8x + 9x * 8x)) = 180
(171 + -171x + (-72x + 72x2)) = 180

Combine like terms: -171x + -72x = -243x
(171 + -243x + 72x2) = 180

Solving
171 + -243x + 72x2 = 180

Solving for variable 'x'.

Reorder the terms:
171 + -180 + -243x + 72x2 = 180 + -180

Combine like terms: 171 + -180 = -9
-9 + -243x + 72x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-9 + -243x + 72x2 = 0

Factor out the Greatest Common Factor (GCF), '9'.
9(-1 + -27x + 8x2) = 0

Ignore the factor 9.
Subproblem 1
Set the factor '(-1 + -27x + 8x2)' equal to zero and attempt to solve:

Simplifying
-1 + -27x + 8x2 = 0

Solving
-1 + -27x + 8x2 = 0

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

Divide each side by '8'.
-0.125 + -3.375x + x2 = 0

Move the constant term to the right:

Add '0.125' to each side of the equation.
-0.125 + -3.375x + 0.125 + x2 = 0 + 0.125

Reorder the terms:
-0.125 + 0.125 + -3.375x + x2 = 0 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + -3.375x + x2 = 0 + 0.125
-3.375x + x2 = 0 + 0.125

Combine like terms: 0 + 0.125 = 0.125
-3.375x + x2 = 0.125

The x term is -3.375x.  Take half its coefficient (-1.6875).
Square it (2.84765625) and add it to both sides.

Add '2.84765625' to each side of the equation.
-3.375x + 2.84765625 + x2 = 0.125 + 2.84765625

Reorder the terms:
2.84765625 + -3.375x + x2 = 0.125 + 2.84765625

Combine like terms: 0.125 + 2.84765625 = 2.97265625
2.84765625 + -3.375x + x2 = 2.97265625

Factor a perfect square on the left side:
(x + -1.6875)(x + -1.6875) = 2.97265625

Calculate the square root of the right side: 1.724139278

Break this problem into two subproblems by setting 
(x + -1.6875) equal to 1.724139278 and -1.724139278.

Subproblem 1
x + -1.6875 = 1.724139278

Simplifying
x + -1.6875 = 1.724139278

Reorder the terms:
-1.6875 + x = 1.724139278

Solving
-1.6875 + x = 1.724139278

Solving for variable 'x'.

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

Add '1.6875' to each side of the equation.
-1.6875 + 1.6875 + x = 1.724139278 + 1.6875

Combine like terms: -1.6875 + 1.6875 = 0.0000
0.0000 + x = 1.724139278 + 1.6875
x = 1.724139278 + 1.6875

Combine like terms: 1.724139278 + 1.6875 = 3.411639278
x = 3.411639278

Simplifying
x = 3.411639278

Subproblem 2
x + -1.6875 = -1.724139278

Simplifying
x + -1.6875 = -1.724139278

Reorder the terms:
-1.6875 + x = -1.724139278

Solving
-1.6875 + x = -1.724139278

Solving for variable 'x'.

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

Add '1.6875' to each side of the equation.
-1.6875 + 1.6875 + x = -1.724139278 + 1.6875

Combine like terms: -1.6875 + 1.6875 = 0.0000
0.0000 + x = -1.724139278 + 1.6875
x = -1.724139278 + 1.6875

Combine like terms: -1.724139278 + 1.6875 = -0.036639278
x = -0.036639278

Simplifying
x = -0.036639278

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.411639278, -0.036639278}
Solution
x = {3.411639278, -0.036639278}