(x+9)(6x+3)=180

Solution for (x+9)(6x+3)=180 equation:

Simplifying
(x + 9)(6x + 3) = 180

Reorder the terms:
(9 + x)(6x + 3) = 180

Reorder the terms:
(9 + x)(3 + 6x) = 180

Multiply (9 + x) * (3 + 6x)
(9(3 + 6x) + x(3 + 6x)) = 180
((3 * 9 + 6x * 9) + x(3 + 6x)) = 180
((27 + 54x) + x(3 + 6x)) = 180
(27 + 54x + (3 * x + 6x * x)) = 180
(27 + 54x + (3x + 6x2)) = 180

Combine like terms: 54x + 3x = 57x
(27 + 57x + 6x2) = 180

Solving
27 + 57x + 6x2 = 180

Solving for variable 'x'.

Reorder the terms:
27 + -180 + 57x + 6x2 = 180 + -180

Combine like terms: 27 + -180 = -153
-153 + 57x + 6x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-153 + 57x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-51 + 19x + 2x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-51 + 19x + 2x2)' equal to zero and attempt to solve:

Simplifying
-51 + 19x + 2x2 = 0

Solving
-51 + 19x + 2x2 = 0

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

Divide each side by '2'.
-25.5 + 9.5x + x2 = 0

Move the constant term to the right:

Add '25.5' to each side of the equation.
-25.5 + 9.5x + 25.5 + x2 = 0 + 25.5

Reorder the terms:
-25.5 + 25.5 + 9.5x + x2 = 0 + 25.5

Combine like terms: -25.5 + 25.5 = 0.0
0.0 + 9.5x + x2 = 0 + 25.5
9.5x + x2 = 0 + 25.5

Combine like terms: 0 + 25.5 = 25.5
9.5x + x2 = 25.5

The x term is 9.5x.  Take half its coefficient (4.75).
Square it (22.5625) and add it to both sides.

Add '22.5625' to each side of the equation.
9.5x + 22.5625 + x2 = 25.5 + 22.5625

Reorder the terms:
22.5625 + 9.5x + x2 = 25.5 + 22.5625

Combine like terms: 25.5 + 22.5625 = 48.0625
22.5625 + 9.5x + x2 = 48.0625

Factor a perfect square on the left side:
(x + 4.75)(x + 4.75) = 48.0625

Calculate the square root of the right side: 6.932712312

Break this problem into two subproblems by setting 
(x + 4.75) equal to 6.932712312 and -6.932712312.

Subproblem 1
x + 4.75 = 6.932712312

Simplifying
x + 4.75 = 6.932712312

Reorder the terms:
4.75 + x = 6.932712312

Solving
4.75 + x = 6.932712312

Solving for variable 'x'.

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

Add '-4.75' to each side of the equation.
4.75 + -4.75 + x = 6.932712312 + -4.75

Combine like terms: 4.75 + -4.75 = 0.00
0.00 + x = 6.932712312 + -4.75
x = 6.932712312 + -4.75

Combine like terms: 6.932712312 + -4.75 = 2.182712312
x = 2.182712312

Simplifying
x = 2.182712312

Subproblem 2
x + 4.75 = -6.932712312

Simplifying
x + 4.75 = -6.932712312

Reorder the terms:
4.75 + x = -6.932712312

Solving
4.75 + x = -6.932712312

Solving for variable 'x'.

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

Add '-4.75' to each side of the equation.
4.75 + -4.75 + x = -6.932712312 + -4.75

Combine like terms: 4.75 + -4.75 = 0.00
0.00 + x = -6.932712312 + -4.75
x = -6.932712312 + -4.75

Combine like terms: -6.932712312 + -4.75 = -11.682712312
x = -11.682712312

Simplifying
x = -11.682712312

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.182712312, -11.682712312}
Solution
x = {2.182712312, -11.682712312}