(9x+3)(7x+1)=180

Solution for (9x+3)(7x+1)=180 equation:

Simplifying
(9x + 3)(7x + 1) = 180

Reorder the terms:
(3 + 9x)(7x + 1) = 180

Reorder the terms:
(3 + 9x)(1 + 7x) = 180

Multiply (3 + 9x) * (1 + 7x)
(3(1 + 7x) + 9x * (1 + 7x)) = 180
((1 * 3 + 7x * 3) + 9x * (1 + 7x)) = 180
((3 + 21x) + 9x * (1 + 7x)) = 180
(3 + 21x + (1 * 9x + 7x * 9x)) = 180
(3 + 21x + (9x + 63x2)) = 180

Combine like terms: 21x + 9x = 30x
(3 + 30x + 63x2) = 180

Solving
3 + 30x + 63x2 = 180

Solving for variable 'x'.

Reorder the terms:
3 + -180 + 30x + 63x2 = 180 + -180

Combine like terms: 3 + -180 = -177
-177 + 30x + 63x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-177 + 30x + 63x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-59 + 10x + 21x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-59 + 10x + 21x2)' equal to zero and attempt to solve:

Simplifying
-59 + 10x + 21x2 = 0

Solving
-59 + 10x + 21x2 = 0

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

Divide each side by '21'.
-2.80952381 + 0.4761904762x + x2 = 0

Move the constant term to the right:

Add '2.80952381' to each side of the equation.
-2.80952381 + 0.4761904762x + 2.80952381 + x2 = 0 + 2.80952381

Reorder the terms:
-2.80952381 + 2.80952381 + 0.4761904762x + x2 = 0 + 2.80952381

Combine like terms: -2.80952381 + 2.80952381 = 0.00000000
0.00000000 + 0.4761904762x + x2 = 0 + 2.80952381
0.4761904762x + x2 = 0 + 2.80952381

Combine like terms: 0 + 2.80952381 = 2.80952381
0.4761904762x + x2 = 2.80952381

The x term is 0.4761904762x.  Take half its coefficient (0.2380952381).
Square it (0.05668934241) and add it to both sides.

Add '0.05668934241' to each side of the equation.
0.4761904762x + 0.05668934241 + x2 = 2.80952381 + 0.05668934241

Reorder the terms:
0.05668934241 + 0.4761904762x + x2 = 2.80952381 + 0.05668934241

Combine like terms: 2.80952381 + 0.05668934241 = 2.86621315241
0.05668934241 + 0.4761904762x + x2 = 2.86621315241

Factor a perfect square on the left side:
(x + 0.2380952381)(x + 0.2380952381) = 2.86621315241

Calculate the square root of the right side: 1.692989413

Break this problem into two subproblems by setting 
(x + 0.2380952381) equal to 1.692989413 and -1.692989413.

Subproblem 1
x + 0.2380952381 = 1.692989413

Simplifying
x + 0.2380952381 = 1.692989413

Reorder the terms:
0.2380952381 + x = 1.692989413

Solving
0.2380952381 + x = 1.692989413

Solving for variable 'x'.

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

Add '-0.2380952381' to each side of the equation.
0.2380952381 + -0.2380952381 + x = 1.692989413 + -0.2380952381

Combine like terms: 0.2380952381 + -0.2380952381 = 0.0000000000
0.0000000000 + x = 1.692989413 + -0.2380952381
x = 1.692989413 + -0.2380952381

Combine like terms: 1.692989413 + -0.2380952381 = 1.4548941749
x = 1.4548941749

Simplifying
x = 1.4548941749

Subproblem 2
x + 0.2380952381 = -1.692989413

Simplifying
x + 0.2380952381 = -1.692989413

Reorder the terms:
0.2380952381 + x = -1.692989413

Solving
0.2380952381 + x = -1.692989413

Solving for variable 'x'.

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

Add '-0.2380952381' to each side of the equation.
0.2380952381 + -0.2380952381 + x = -1.692989413 + -0.2380952381

Combine like terms: 0.2380952381 + -0.2380952381 = 0.0000000000
0.0000000000 + x = -1.692989413 + -0.2380952381
x = -1.692989413 + -0.2380952381

Combine like terms: -1.692989413 + -0.2380952381 = -1.9310846511
x = -1.9310846511

Simplifying
x = -1.9310846511

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.4548941749, -1.9310846511}
Solution
x = {1.4548941749, -1.9310846511}