(3x+33)(7x+5)=180

Solution for (3x+33)(7x+5)=180 equation:

Simplifying
(3x + 33)(7x + 5) = 180

Reorder the terms:
(33 + 3x)(7x + 5) = 180

Reorder the terms:
(33 + 3x)(5 + 7x) = 180

Multiply (33 + 3x) * (5 + 7x)
(33(5 + 7x) + 3x * (5 + 7x)) = 180
((5 * 33 + 7x * 33) + 3x * (5 + 7x)) = 180
((165 + 231x) + 3x * (5 + 7x)) = 180
(165 + 231x + (5 * 3x + 7x * 3x)) = 180
(165 + 231x + (15x + 21x2)) = 180

Combine like terms: 231x + 15x = 246x
(165 + 246x + 21x2) = 180

Solving
165 + 246x + 21x2 = 180

Solving for variable 'x'.

Reorder the terms:
165 + -180 + 246x + 21x2 = 180 + -180

Combine like terms: 165 + -180 = -15
-15 + 246x + 21x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-15 + 246x + 21x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-5 + 82x + 7x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-5 + 82x + 7x2)' equal to zero and attempt to solve:

Simplifying
-5 + 82x + 7x2 = 0

Solving
-5 + 82x + 7x2 = 0

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

Divide each side by '7'.
-0.7142857143 + 11.71428571x + x2 = 0

Move the constant term to the right:

Add '0.7142857143' to each side of the equation.
-0.7142857143 + 11.71428571x + 0.7142857143 + x2 = 0 + 0.7142857143

Reorder the terms:
-0.7142857143 + 0.7142857143 + 11.71428571x + x2 = 0 + 0.7142857143

Combine like terms: -0.7142857143 + 0.7142857143 = 0.0000000000
0.0000000000 + 11.71428571x + x2 = 0 + 0.7142857143
11.71428571x + x2 = 0 + 0.7142857143

Combine like terms: 0 + 0.7142857143 = 0.7142857143
11.71428571x + x2 = 0.7142857143

The x term is 11.71428571x.  Take half its coefficient (5.857142855).
Square it (34.30612242) and add it to both sides.

Add '34.30612242' to each side of the equation.
11.71428571x + 34.30612242 + x2 = 0.7142857143 + 34.30612242

Reorder the terms:
34.30612242 + 11.71428571x + x2 = 0.7142857143 + 34.30612242

Combine like terms: 0.7142857143 + 34.30612242 = 35.0204081343
34.30612242 + 11.71428571x + x2 = 35.0204081343

Factor a perfect square on the left side:
(x + 5.857142855)(x + 5.857142855) = 35.0204081343

Calculate the square root of the right side: 5.917804334

Break this problem into two subproblems by setting 
(x + 5.857142855) equal to 5.917804334 and -5.917804334.

Subproblem 1
x + 5.857142855 = 5.917804334

Simplifying
x + 5.857142855 = 5.917804334

Reorder the terms:
5.857142855 + x = 5.917804334

Solving
5.857142855 + x = 5.917804334

Solving for variable 'x'.

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

Add '-5.857142855' to each side of the equation.
5.857142855 + -5.857142855 + x = 5.917804334 + -5.857142855

Combine like terms: 5.857142855 + -5.857142855 = 0.000000000
0.000000000 + x = 5.917804334 + -5.857142855
x = 5.917804334 + -5.857142855

Combine like terms: 5.917804334 + -5.857142855 = 0.060661479
x = 0.060661479

Simplifying
x = 0.060661479

Subproblem 2
x + 5.857142855 = -5.917804334

Simplifying
x + 5.857142855 = -5.917804334

Reorder the terms:
5.857142855 + x = -5.917804334

Solving
5.857142855 + x = -5.917804334

Solving for variable 'x'.

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

Add '-5.857142855' to each side of the equation.
5.857142855 + -5.857142855 + x = -5.917804334 + -5.857142855

Combine like terms: 5.857142855 + -5.857142855 = 0.000000000
0.000000000 + x = -5.917804334 + -5.857142855
x = -5.917804334 + -5.857142855

Combine like terms: -5.917804334 + -5.857142855 = -11.774947189
x = -11.774947189

Simplifying
x = -11.774947189

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.060661479, -11.774947189}
Solution
x = {0.060661479, -11.774947189}