(2x+5)(3x-23)=180

Solution for (2x+5)(3x-23)=180 equation:

Simplifying
(2x + 5)(3x + -23) = 180

Reorder the terms:
(5 + 2x)(3x + -23) = 180

Reorder the terms:
(5 + 2x)(-23 + 3x) = 180

Multiply (5 + 2x) * (-23 + 3x)
(5(-23 + 3x) + 2x * (-23 + 3x)) = 180
((-23 * 5 + 3x * 5) + 2x * (-23 + 3x)) = 180
((-115 + 15x) + 2x * (-23 + 3x)) = 180
(-115 + 15x + (-23 * 2x + 3x * 2x)) = 180
(-115 + 15x + (-46x + 6x2)) = 180

Combine like terms: 15x + -46x = -31x
(-115 + -31x + 6x2) = 180

Solving
-115 + -31x + 6x2 = 180

Solving for variable 'x'.

Reorder the terms:
-115 + -180 + -31x + 6x2 = 180 + -180

Combine like terms: -115 + -180 = -295
-295 + -31x + 6x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-295 + -31x + 6x2 = 0

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

Divide each side by '6'.
-49.16666667 + -5.166666667x + x2 = 0

Move the constant term to the right:

Add '49.16666667' to each side of the equation.
-49.16666667 + -5.166666667x + 49.16666667 + x2 = 0 + 49.16666667

Reorder the terms:
-49.16666667 + 49.16666667 + -5.166666667x + x2 = 0 + 49.16666667

Combine like terms: -49.16666667 + 49.16666667 = 0.00000000
0.00000000 + -5.166666667x + x2 = 0 + 49.16666667
-5.166666667x + x2 = 0 + 49.16666667

Combine like terms: 0 + 49.16666667 = 49.16666667
-5.166666667x + x2 = 49.16666667

The x term is -5.166666667x.  Take half its coefficient (-2.583333334).
Square it (6.673611115) and add it to both sides.

Add '6.673611115' to each side of the equation.
-5.166666667x + 6.673611115 + x2 = 49.16666667 + 6.673611115

Reorder the terms:
6.673611115 + -5.166666667x + x2 = 49.16666667 + 6.673611115

Combine like terms: 49.16666667 + 6.673611115 = 55.840277785
6.673611115 + -5.166666667x + x2 = 55.840277785

Factor a perfect square on the left side:
(x + -2.583333334)(x + -2.583333334) = 55.840277785

Calculate the square root of the right side: 7.472635264

Break this problem into two subproblems by setting 
(x + -2.583333334) equal to 7.472635264 and -7.472635264.

Subproblem 1
x + -2.583333334 = 7.472635264

Simplifying
x + -2.583333334 = 7.472635264

Reorder the terms:
-2.583333334 + x = 7.472635264

Solving
-2.583333334 + x = 7.472635264

Solving for variable 'x'.

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

Add '2.583333334' to each side of the equation.
-2.583333334 + 2.583333334 + x = 7.472635264 + 2.583333334

Combine like terms: -2.583333334 + 2.583333334 = 0.000000000
0.000000000 + x = 7.472635264 + 2.583333334
x = 7.472635264 + 2.583333334

Combine like terms: 7.472635264 + 2.583333334 = 10.055968598
x = 10.055968598

Simplifying
x = 10.055968598

Subproblem 2
x + -2.583333334 = -7.472635264

Simplifying
x + -2.583333334 = -7.472635264

Reorder the terms:
-2.583333334 + x = -7.472635264

Solving
-2.583333334 + x = -7.472635264

Solving for variable 'x'.

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

Add '2.583333334' to each side of the equation.
-2.583333334 + 2.583333334 + x = -7.472635264 + 2.583333334

Combine like terms: -2.583333334 + 2.583333334 = 0.000000000
0.000000000 + x = -7.472635264 + 2.583333334
x = -7.472635264 + 2.583333334

Combine like terms: -7.472635264 + 2.583333334 = -4.88930193
x = -4.88930193

Simplifying
x = -4.88930193

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.055968598, -4.88930193}