(22x+4)(15x+5)+120=180

Solution for (22x+4)(15x+5)+120=180 equation:

Simplifying
(22x + 4)(15x + 5) + 120 = 180

Reorder the terms:
(4 + 22x)(15x + 5) + 120 = 180

Reorder the terms:
(4 + 22x)(5 + 15x) + 120 = 180

Multiply (4 + 22x) * (5 + 15x)
(4(5 + 15x) + 22x * (5 + 15x)) + 120 = 180
((5 * 4 + 15x * 4) + 22x * (5 + 15x)) + 120 = 180
((20 + 60x) + 22x * (5 + 15x)) + 120 = 180
(20 + 60x + (5 * 22x + 15x * 22x)) + 120 = 180
(20 + 60x + (110x + 330x2)) + 120 = 180

Combine like terms: 60x + 110x = 170x
(20 + 170x + 330x2) + 120 = 180

Reorder the terms:
20 + 120 + 170x + 330x2 = 180

Combine like terms: 20 + 120 = 140
140 + 170x + 330x2 = 180

Solving
140 + 170x + 330x2 = 180

Solving for variable 'x'.

Reorder the terms:
140 + -180 + 170x + 330x2 = 180 + -180

Combine like terms: 140 + -180 = -40
-40 + 170x + 330x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-40 + 170x + 330x2 = 0

Factor out the Greatest Common Factor (GCF), '10'.
10(-4 + 17x + 33x2) = 0

Ignore the factor 10.
Subproblem 1
Set the factor '(-4 + 17x + 33x2)' equal to zero and attempt to solve:

Simplifying
-4 + 17x + 33x2 = 0

Solving
-4 + 17x + 33x2 = 0

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

Divide each side by '33'.
-0.1212121212 + 0.5151515152x + x2 = 0

Move the constant term to the right:

Add '0.1212121212' to each side of the equation.
-0.1212121212 + 0.5151515152x + 0.1212121212 + x2 = 0 + 0.1212121212

Reorder the terms:
-0.1212121212 + 0.1212121212 + 0.5151515152x + x2 = 0 + 0.1212121212

Combine like terms: -0.1212121212 + 0.1212121212 = 0.0000000000
0.0000000000 + 0.5151515152x + x2 = 0 + 0.1212121212
0.5151515152x + x2 = 0 + 0.1212121212

Combine like terms: 0 + 0.1212121212 = 0.1212121212
0.5151515152x + x2 = 0.1212121212

The x term is 0.5151515152x.  Take half its coefficient (0.2575757576).
Square it (0.06634527090) and add it to both sides.

Add '0.06634527090' to each side of the equation.
0.5151515152x + 0.06634527090 + x2 = 0.1212121212 + 0.06634527090

Reorder the terms:
0.06634527090 + 0.5151515152x + x2 = 0.1212121212 + 0.06634527090

Combine like terms: 0.1212121212 + 0.06634527090 = 0.1875573921
0.06634527090 + 0.5151515152x + x2 = 0.1875573921

Factor a perfect square on the left side:
(x + 0.2575757576)(x + 0.2575757576) = 0.1875573921

Calculate the square root of the right side: 0.433078968

Break this problem into two subproblems by setting 
(x + 0.2575757576) equal to 0.433078968 and -0.433078968.

Subproblem 1
x + 0.2575757576 = 0.433078968

Simplifying
x + 0.2575757576 = 0.433078968

Reorder the terms:
0.2575757576 + x = 0.433078968

Solving
0.2575757576 + x = 0.433078968

Solving for variable 'x'.

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

Add '-0.2575757576' to each side of the equation.
0.2575757576 + -0.2575757576 + x = 0.433078968 + -0.2575757576

Combine like terms: 0.2575757576 + -0.2575757576 = 0.0000000000
0.0000000000 + x = 0.433078968 + -0.2575757576
x = 0.433078968 + -0.2575757576

Combine like terms: 0.433078968 + -0.2575757576 = 0.1755032104
x = 0.1755032104

Simplifying
x = 0.1755032104

Subproblem 2
x + 0.2575757576 = -0.433078968

Simplifying
x + 0.2575757576 = -0.433078968

Reorder the terms:
0.2575757576 + x = -0.433078968

Solving
0.2575757576 + x = -0.433078968

Solving for variable 'x'.

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

Add '-0.2575757576' to each side of the equation.
0.2575757576 + -0.2575757576 + x = -0.433078968 + -0.2575757576

Combine like terms: 0.2575757576 + -0.2575757576 = 0.0000000000
0.0000000000 + x = -0.433078968 + -0.2575757576
x = -0.433078968 + -0.2575757576

Combine like terms: -0.433078968 + -0.2575757576 = -0.6906547256
x = -0.6906547256

Simplifying
x = -0.6906547256

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.1755032104, -0.6906547256}
Solution
x = {0.1755032104, -0.6906547256}