(5x+1)(12x+9)=180

Solution for (5x+1)(12x+9)=180 equation:

Simplifying
(5x + 1)(12x + 9) = 180

Reorder the terms:
(1 + 5x)(12x + 9) = 180

Reorder the terms:
(1 + 5x)(9 + 12x) = 180

Multiply (1 + 5x) * (9 + 12x)
(1(9 + 12x) + 5x * (9 + 12x)) = 180
((9 * 1 + 12x * 1) + 5x * (9 + 12x)) = 180
((9 + 12x) + 5x * (9 + 12x)) = 180
(9 + 12x + (9 * 5x + 12x * 5x)) = 180
(9 + 12x + (45x + 60x2)) = 180

Combine like terms: 12x + 45x = 57x
(9 + 57x + 60x2) = 180

Solving
9 + 57x + 60x2 = 180

Solving for variable 'x'.

Reorder the terms:
9 + -180 + 57x + 60x2 = 180 + -180

Combine like terms: 9 + -180 = -171
-171 + 57x + 60x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-171 + 57x + 60x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-57 + 19x + 20x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-57 + 19x + 20x2)' equal to zero and attempt to solve:

Simplifying
-57 + 19x + 20x2 = 0

Solving
-57 + 19x + 20x2 = 0

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

Divide each side by '20'.
-2.85 + 0.95x + x2 = 0.0

Move the constant term to the right:

Add '2.85' to each side of the equation.
-2.85 + 0.95x + 2.85 + x2 = 0.0 + 2.85

Reorder the terms:
-2.85 + 2.85 + 0.95x + x2 = 0.0 + 2.85

Combine like terms: -2.85 + 2.85 = 0.00
0.00 + 0.95x + x2 = 0.0 + 2.85
0.95x + x2 = 0.0 + 2.85

Combine like terms: 0.0 + 2.85 = 2.85
0.95x + x2 = 2.85

The x term is 0.95x.  Take half its coefficient (0.475).
Square it (0.225625) and add it to both sides.

Add '0.225625' to each side of the equation.
0.95x + 0.225625 + x2 = 2.85 + 0.225625

Reorder the terms:
0.225625 + 0.95x + x2 = 2.85 + 0.225625

Combine like terms: 2.85 + 0.225625 = 3.075625
0.225625 + 0.95x + x2 = 3.075625

Factor a perfect square on the left side:
(x + 0.475)(x + 0.475) = 3.075625

Calculate the square root of the right side: 1.753745991

Break this problem into two subproblems by setting 
(x + 0.475) equal to 1.753745991 and -1.753745991.

Subproblem 1
x + 0.475 = 1.753745991

Simplifying
x + 0.475 = 1.753745991

Reorder the terms:
0.475 + x = 1.753745991

Solving
0.475 + x = 1.753745991

Solving for variable 'x'.

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

Add '-0.475' to each side of the equation.
0.475 + -0.475 + x = 1.753745991 + -0.475

Combine like terms: 0.475 + -0.475 = 0.000
0.000 + x = 1.753745991 + -0.475
x = 1.753745991 + -0.475

Combine like terms: 1.753745991 + -0.475 = 1.278745991
x = 1.278745991

Simplifying
x = 1.278745991

Subproblem 2
x + 0.475 = -1.753745991

Simplifying
x + 0.475 = -1.753745991

Reorder the terms:
0.475 + x = -1.753745991

Solving
0.475 + x = -1.753745991

Solving for variable 'x'.

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

Add '-0.475' to each side of the equation.
0.475 + -0.475 + x = -1.753745991 + -0.475

Combine like terms: 0.475 + -0.475 = 0.000
0.000 + x = -1.753745991 + -0.475
x = -1.753745991 + -0.475

Combine like terms: -1.753745991 + -0.475 = -2.228745991
x = -2.228745991

Simplifying
x = -2.228745991

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.278745991, -2.228745991}
Solution
x = {1.278745991, -2.228745991}