(18x+28)(7x+27)=180

Solution for (18x+28)(7x+27)=180 equation:

Simplifying
(18x + 28)(7x + 27) = 180

Reorder the terms:
(28 + 18x)(7x + 27) = 180

Reorder the terms:
(28 + 18x)(27 + 7x) = 180

Multiply (28 + 18x) * (27 + 7x)
(28(27 + 7x) + 18x * (27 + 7x)) = 180
((27 * 28 + 7x * 28) + 18x * (27 + 7x)) = 180
((756 + 196x) + 18x * (27 + 7x)) = 180
(756 + 196x + (27 * 18x + 7x * 18x)) = 180
(756 + 196x + (486x + 126x2)) = 180

Combine like terms: 196x + 486x = 682x
(756 + 682x + 126x2) = 180

Solving
756 + 682x + 126x2 = 180

Solving for variable 'x'.

Reorder the terms:
756 + -180 + 682x + 126x2 = 180 + -180

Combine like terms: 756 + -180 = 576
576 + 682x + 126x2 = 180 + -180

Combine like terms: 180 + -180 = 0
576 + 682x + 126x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(288 + 341x + 63x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(288 + 341x + 63x2)' equal to zero and attempt to solve:

Simplifying
288 + 341x + 63x2 = 0

Solving
288 + 341x + 63x2 = 0

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

Divide each side by '63'.
4.571428571 + 5.412698413x + x2 = 0

Move the constant term to the right:

Add '-4.571428571' to each side of the equation.
4.571428571 + 5.412698413x + -4.571428571 + x2 = 0 + -4.571428571

Reorder the terms:
4.571428571 + -4.571428571 + 5.412698413x + x2 = 0 + -4.571428571

Combine like terms: 4.571428571 + -4.571428571 = 0.000000000
0.000000000 + 5.412698413x + x2 = 0 + -4.571428571
5.412698413x + x2 = 0 + -4.571428571

Combine like terms: 0 + -4.571428571 = -4.571428571
5.412698413x + x2 = -4.571428571

The x term is 5.412698413x.  Take half its coefficient (2.706349207).
Square it (7.324326030) and add it to both sides.

Add '7.324326030' to each side of the equation.
5.412698413x + 7.324326030 + x2 = -4.571428571 + 7.324326030

Reorder the terms:
7.324326030 + 5.412698413x + x2 = -4.571428571 + 7.324326030

Combine like terms: -4.571428571 + 7.324326030 = 2.752897459
7.324326030 + 5.412698413x + x2 = 2.752897459

Factor a perfect square on the left side:
(x + 2.706349207)(x + 2.706349207) = 2.752897459

Calculate the square root of the right side: 1.659185782

Break this problem into two subproblems by setting 
(x + 2.706349207) equal to 1.659185782 and -1.659185782.

Subproblem 1
x + 2.706349207 = 1.659185782

Simplifying
x + 2.706349207 = 1.659185782

Reorder the terms:
2.706349207 + x = 1.659185782

Solving
2.706349207 + x = 1.659185782

Solving for variable 'x'.

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

Add '-2.706349207' to each side of the equation.
2.706349207 + -2.706349207 + x = 1.659185782 + -2.706349207

Combine like terms: 2.706349207 + -2.706349207 = 0.000000000
0.000000000 + x = 1.659185782 + -2.706349207
x = 1.659185782 + -2.706349207

Combine like terms: 1.659185782 + -2.706349207 = -1.047163425
x = -1.047163425

Simplifying
x = -1.047163425

Subproblem 2
x + 2.706349207 = -1.659185782

Simplifying
x + 2.706349207 = -1.659185782

Reorder the terms:
2.706349207 + x = -1.659185782

Solving
2.706349207 + x = -1.659185782

Solving for variable 'x'.

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

Add '-2.706349207' to each side of the equation.
2.706349207 + -2.706349207 + x = -1.659185782 + -2.706349207

Combine like terms: 2.706349207 + -2.706349207 = 0.000000000
0.000000000 + x = -1.659185782 + -2.706349207
x = -1.659185782 + -2.706349207

Combine like terms: -1.659185782 + -2.706349207 = -4.365534989
x = -4.365534989

Simplifying
x = -4.365534989

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.047163425, -4.365534989}
Solution
x = {-1.047163425, -4.365534989}