(20x+2)(15x+3)=180

Solution for (20x+2)(15x+3)=180 equation:

Simplifying
(20x + 2)(15x + 3) = 180

Reorder the terms:
(2 + 20x)(15x + 3) = 180

Reorder the terms:
(2 + 20x)(3 + 15x) = 180

Multiply (2 + 20x) * (3 + 15x)
(2(3 + 15x) + 20x * (3 + 15x)) = 180
((3 * 2 + 15x * 2) + 20x * (3 + 15x)) = 180
((6 + 30x) + 20x * (3 + 15x)) = 180
(6 + 30x + (3 * 20x + 15x * 20x)) = 180
(6 + 30x + (60x + 300x2)) = 180

Combine like terms: 30x + 60x = 90x
(6 + 90x + 300x2) = 180

Solving
6 + 90x + 300x2 = 180

Solving for variable 'x'.

Reorder the terms:
6 + -180 + 90x + 300x2 = 180 + -180

Combine like terms: 6 + -180 = -174
-174 + 90x + 300x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-174 + 90x + 300x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-29 + 15x + 50x2) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-29 + 15x + 50x2)' equal to zero and attempt to solve:

Simplifying
-29 + 15x + 50x2 = 0

Solving
-29 + 15x + 50x2 = 0

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

Divide each side by '50'.
-0.58 + 0.3x + x2 = 0.0

Move the constant term to the right:

Add '0.58' to each side of the equation.
-0.58 + 0.3x + 0.58 + x2 = 0.0 + 0.58

Reorder the terms:
-0.58 + 0.58 + 0.3x + x2 = 0.0 + 0.58

Combine like terms: -0.58 + 0.58 = 0.00
0.00 + 0.3x + x2 = 0.0 + 0.58
0.3x + x2 = 0.0 + 0.58

Combine like terms: 0.0 + 0.58 = 0.58
0.3x + x2 = 0.58

The x term is 0.3x.  Take half its coefficient (0.15).
Square it (0.0225) and add it to both sides.

Add '0.0225' to each side of the equation.
0.3x + 0.0225 + x2 = 0.58 + 0.0225

Reorder the terms:
0.0225 + 0.3x + x2 = 0.58 + 0.0225

Combine like terms: 0.58 + 0.0225 = 0.6025
0.0225 + 0.3x + x2 = 0.6025

Factor a perfect square on the left side:
(x + 0.15)(x + 0.15) = 0.6025

Calculate the square root of the right side: 0.776208735

Break this problem into two subproblems by setting 
(x + 0.15) equal to 0.776208735 and -0.776208735.

Subproblem 1
x + 0.15 = 0.776208735

Simplifying
x + 0.15 = 0.776208735

Reorder the terms:
0.15 + x = 0.776208735

Solving
0.15 + x = 0.776208735

Solving for variable 'x'.

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

Add '-0.15' to each side of the equation.
0.15 + -0.15 + x = 0.776208735 + -0.15

Combine like terms: 0.15 + -0.15 = 0.00
0.00 + x = 0.776208735 + -0.15
x = 0.776208735 + -0.15

Combine like terms: 0.776208735 + -0.15 = 0.626208735
x = 0.626208735

Simplifying
x = 0.626208735

Subproblem 2
x + 0.15 = -0.776208735

Simplifying
x + 0.15 = -0.776208735

Reorder the terms:
0.15 + x = -0.776208735

Solving
0.15 + x = -0.776208735

Solving for variable 'x'.

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

Add '-0.15' to each side of the equation.
0.15 + -0.15 + x = -0.776208735 + -0.15

Combine like terms: 0.15 + -0.15 = 0.00
0.00 + x = -0.776208735 + -0.15
x = -0.776208735 + -0.15

Combine like terms: -0.776208735 + -0.15 = -0.926208735
x = -0.926208735

Simplifying
x = -0.926208735

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.626208735, -0.926208735}
Solution
x = {0.626208735, -0.926208735}