(2x+22)(3x)=180

Solution for (2x+22)(3x)=180 equation:

Simplifying
(2x + 22)(3x) = 180

Reorder the terms:
(22 + 2x)(3x) = 180

Remove parenthesis around (3x)
(22 + 2x) * 3x = 180

Reorder the terms for easier multiplication:
3x(22 + 2x) = 180
(22 * 3x + 2x * 3x) = 180
(66x + 6x2) = 180

Solving
66x + 6x2 = 180

Solving for variable 'x'.

Reorder the terms:
-180 + 66x + 6x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + 66x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-30 + 11x + x2) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-30 + 11x + x2)' equal to zero and attempt to solve:

Simplifying
-30 + 11x + x2 = 0

Solving
-30 + 11x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + 11x + 30 + x2 = 0 + 30

Reorder the terms:
-30 + 30 + 11x + x2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + 11x + x2 = 0 + 30
11x + x2 = 0 + 30

Combine like terms: 0 + 30 = 30
11x + x2 = 30

The x term is 11x.  Take half its coefficient (5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
11x + 30.25 + x2 = 30 + 30.25

Reorder the terms:
30.25 + 11x + x2 = 30 + 30.25

Combine like terms: 30 + 30.25 = 60.25
30.25 + 11x + x2 = 60.25

Factor a perfect square on the left side:
(x + 5.5)(x + 5.5) = 60.25

Calculate the square root of the right side: 7.762087348

Break this problem into two subproblems by setting 
(x + 5.5) equal to 7.762087348 and -7.762087348.

Subproblem 1
x + 5.5 = 7.762087348

Simplifying
x + 5.5 = 7.762087348

Reorder the terms:
5.5 + x = 7.762087348

Solving
5.5 + x = 7.762087348

Solving for variable 'x'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + x = 7.762087348 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + x = 7.762087348 + -5.5
x = 7.762087348 + -5.5

Combine like terms: 7.762087348 + -5.5 = 2.262087348
x = 2.262087348

Simplifying
x = 2.262087348

Subproblem 2
x + 5.5 = -7.762087348

Simplifying
x + 5.5 = -7.762087348

Reorder the terms:
5.5 + x = -7.762087348

Solving
5.5 + x = -7.762087348

Solving for variable 'x'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + x = -7.762087348 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + x = -7.762087348 + -5.5
x = -7.762087348 + -5.5

Combine like terms: -7.762087348 + -5.5 = -13.262087348
x = -13.262087348

Simplifying
x = -13.262087348

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.262087348, -13.262087348}
Solution
x = {2.262087348, -13.262087348}