(12x-54)(7x+26)=180

Solution for (12x-54)(7x+26)=180 equation:

Simplifying
(12x + -54)(7x + 26) = 180

Reorder the terms:
(-54 + 12x)(7x + 26) = 180

Reorder the terms:
(-54 + 12x)(26 + 7x) = 180

Multiply (-54 + 12x) * (26 + 7x)
(-54(26 + 7x) + 12x * (26 + 7x)) = 180
((26 * -54 + 7x * -54) + 12x * (26 + 7x)) = 180
((-1404 + -378x) + 12x * (26 + 7x)) = 180
(-1404 + -378x + (26 * 12x + 7x * 12x)) = 180
(-1404 + -378x + (312x + 84x2)) = 180

Combine like terms: -378x + 312x = -66x
(-1404 + -66x + 84x2) = 180

Solving
-1404 + -66x + 84x2 = 180

Solving for variable 'x'.

Reorder the terms:
-1404 + -180 + -66x + 84x2 = 180 + -180

Combine like terms: -1404 + -180 = -1584
-1584 + -66x + 84x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-1584 + -66x + 84x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-264 + -11x + 14x2) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-264 + -11x + 14x2)' equal to zero and attempt to solve:

Simplifying
-264 + -11x + 14x2 = 0

Solving
-264 + -11x + 14x2 = 0

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

Divide each side by '14'.
-18.85714286 + -0.7857142857x + x2 = 0

Move the constant term to the right:

Add '18.85714286' to each side of the equation.
-18.85714286 + -0.7857142857x + 18.85714286 + x2 = 0 + 18.85714286

Reorder the terms:
-18.85714286 + 18.85714286 + -0.7857142857x + x2 = 0 + 18.85714286

Combine like terms: -18.85714286 + 18.85714286 = 0.00000000
0.00000000 + -0.7857142857x + x2 = 0 + 18.85714286
-0.7857142857x + x2 = 0 + 18.85714286

Combine like terms: 0 + 18.85714286 = 18.85714286
-0.7857142857x + x2 = 18.85714286

The x term is -0.7857142857x.  Take half its coefficient (-0.3928571429).
Square it (0.1543367347) and add it to both sides.

Add '0.1543367347' to each side of the equation.
-0.7857142857x + 0.1543367347 + x2 = 18.85714286 + 0.1543367347

Reorder the terms:
0.1543367347 + -0.7857142857x + x2 = 18.85714286 + 0.1543367347

Combine like terms: 18.85714286 + 0.1543367347 = 19.0114795947
0.1543367347 + -0.7857142857x + x2 = 19.0114795947

Factor a perfect square on the left side:
(x + -0.3928571429)(x + -0.3928571429) = 19.0114795947

Calculate the square root of the right side: 4.360215545

Break this problem into two subproblems by setting 
(x + -0.3928571429) equal to 4.360215545 and -4.360215545.

Subproblem 1
x + -0.3928571429 = 4.360215545

Simplifying
x + -0.3928571429 = 4.360215545

Reorder the terms:
-0.3928571429 + x = 4.360215545

Solving
-0.3928571429 + x = 4.360215545

Solving for variable 'x'.

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

Add '0.3928571429' to each side of the equation.
-0.3928571429 + 0.3928571429 + x = 4.360215545 + 0.3928571429

Combine like terms: -0.3928571429 + 0.3928571429 = 0.0000000000
0.0000000000 + x = 4.360215545 + 0.3928571429
x = 4.360215545 + 0.3928571429

Combine like terms: 4.360215545 + 0.3928571429 = 4.7530726879
x = 4.7530726879

Simplifying
x = 4.7530726879

Subproblem 2
x + -0.3928571429 = -4.360215545

Simplifying
x + -0.3928571429 = -4.360215545

Reorder the terms:
-0.3928571429 + x = -4.360215545

Solving
-0.3928571429 + x = -4.360215545

Solving for variable 'x'.

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

Add '0.3928571429' to each side of the equation.
-0.3928571429 + 0.3928571429 + x = -4.360215545 + 0.3928571429

Combine like terms: -0.3928571429 + 0.3928571429 = 0.0000000000
0.0000000000 + x = -4.360215545 + 0.3928571429
x = -4.360215545 + 0.3928571429

Combine like terms: -4.360215545 + 0.3928571429 = -3.9673584021
x = -3.9673584021

Simplifying
x = -3.9673584021

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.7530726879, -3.9673584021}
Solution
x = {4.7530726879, -3.9673584021}