(5x+3)(2x+8)=180

Solution for (5x+3)(2x+8)=180 equation:

Simplifying
(5x + 3)(2x + 8) = 180

Reorder the terms:
(3 + 5x)(2x + 8) = 180

Reorder the terms:
(3 + 5x)(8 + 2x) = 180

Multiply (3 + 5x) * (8 + 2x)
(3(8 + 2x) + 5x * (8 + 2x)) = 180
((8 * 3 + 2x * 3) + 5x * (8 + 2x)) = 180
((24 + 6x) + 5x * (8 + 2x)) = 180
(24 + 6x + (8 * 5x + 2x * 5x)) = 180
(24 + 6x + (40x + 10x2)) = 180

Combine like terms: 6x + 40x = 46x
(24 + 46x + 10x2) = 180

Solving
24 + 46x + 10x2 = 180

Solving for variable 'x'.

Reorder the terms:
24 + -180 + 46x + 10x2 = 180 + -180

Combine like terms: 24 + -180 = -156
-156 + 46x + 10x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-156 + 46x + 10x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-78 + 23x + 5x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-78 + 23x + 5x2)' equal to zero and attempt to solve:

Simplifying
-78 + 23x + 5x2 = 0

Solving
-78 + 23x + 5x2 = 0

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

Divide each side by '5'.
-15.6 + 4.6x + x2 = 0

Move the constant term to the right:

Add '15.6' to each side of the equation.
-15.6 + 4.6x + 15.6 + x2 = 0 + 15.6

Reorder the terms:
-15.6 + 15.6 + 4.6x + x2 = 0 + 15.6

Combine like terms: -15.6 + 15.6 = 0.0
0.0 + 4.6x + x2 = 0 + 15.6
4.6x + x2 = 0 + 15.6

Combine like terms: 0 + 15.6 = 15.6
4.6x + x2 = 15.6

The x term is 4.6x.  Take half its coefficient (2.3).
Square it (5.29) and add it to both sides.

Add '5.29' to each side of the equation.
4.6x + 5.29 + x2 = 15.6 + 5.29

Reorder the terms:
5.29 + 4.6x + x2 = 15.6 + 5.29

Combine like terms: 15.6 + 5.29 = 20.89
5.29 + 4.6x + x2 = 20.89

Factor a perfect square on the left side:
(x + 2.3)(x + 2.3) = 20.89

Calculate the square root of the right side: 4.570557953

Break this problem into two subproblems by setting 
(x + 2.3) equal to 4.570557953 and -4.570557953.

Subproblem 1
x + 2.3 = 4.570557953

Simplifying
x + 2.3 = 4.570557953

Reorder the terms:
2.3 + x = 4.570557953

Solving
2.3 + x = 4.570557953

Solving for variable 'x'.

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

Add '-2.3' to each side of the equation.
2.3 + -2.3 + x = 4.570557953 + -2.3

Combine like terms: 2.3 + -2.3 = 0.0
0.0 + x = 4.570557953 + -2.3
x = 4.570557953 + -2.3

Combine like terms: 4.570557953 + -2.3 = 2.270557953
x = 2.270557953

Simplifying
x = 2.270557953

Subproblem 2
x + 2.3 = -4.570557953

Simplifying
x + 2.3 = -4.570557953

Reorder the terms:
2.3 + x = -4.570557953

Solving
2.3 + x = -4.570557953

Solving for variable 'x'.

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

Add '-2.3' to each side of the equation.
2.3 + -2.3 + x = -4.570557953 + -2.3

Combine like terms: 2.3 + -2.3 = 0.0
0.0 + x = -4.570557953 + -2.3
x = -4.570557953 + -2.3

Combine like terms: -4.570557953 + -2.3 = -6.870557953
x = -6.870557953

Simplifying
x = -6.870557953

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.270557953, -6.870557953}
Solution
x = {2.270557953, -6.870557953}