(2x+5)(3x-18)=117

Solution for (2x+5)(3x-18)=117 equation:

Simplifying
(2x + 5)(3x + -18) = 117

Reorder the terms:
(5 + 2x)(3x + -18) = 117

Reorder the terms:
(5 + 2x)(-18 + 3x) = 117

Multiply (5 + 2x) * (-18 + 3x)
(5(-18 + 3x) + 2x * (-18 + 3x)) = 117
((-18 * 5 + 3x * 5) + 2x * (-18 + 3x)) = 117
((-90 + 15x) + 2x * (-18 + 3x)) = 117
(-90 + 15x + (-18 * 2x + 3x * 2x)) = 117
(-90 + 15x + (-36x + 6x2)) = 117

Combine like terms: 15x + -36x = -21x
(-90 + -21x + 6x2) = 117

Solving
-90 + -21x + 6x2 = 117

Solving for variable 'x'.

Reorder the terms:
-90 + -117 + -21x + 6x2 = 117 + -117

Combine like terms: -90 + -117 = -207
-207 + -21x + 6x2 = 117 + -117

Combine like terms: 117 + -117 = 0
-207 + -21x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-69 + -7x + 2x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-69 + -7x + 2x2)' equal to zero and attempt to solve:

Simplifying
-69 + -7x + 2x2 = 0

Solving
-69 + -7x + 2x2 = 0

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

Divide each side by '2'.
-34.5 + -3.5x + x2 = 0

Move the constant term to the right:

Add '34.5' to each side of the equation.
-34.5 + -3.5x + 34.5 + x2 = 0 + 34.5

Reorder the terms:
-34.5 + 34.5 + -3.5x + x2 = 0 + 34.5

Combine like terms: -34.5 + 34.5 = 0.0
0.0 + -3.5x + x2 = 0 + 34.5
-3.5x + x2 = 0 + 34.5

Combine like terms: 0 + 34.5 = 34.5
-3.5x + x2 = 34.5

The x term is -3.5x.  Take half its coefficient (-1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
-3.5x + 3.0625 + x2 = 34.5 + 3.0625

Reorder the terms:
3.0625 + -3.5x + x2 = 34.5 + 3.0625

Combine like terms: 34.5 + 3.0625 = 37.5625
3.0625 + -3.5x + x2 = 37.5625

Factor a perfect square on the left side:
(x + -1.75)(x + -1.75) = 37.5625

Calculate the square root of the right side: 6.128825336

Break this problem into two subproblems by setting 
(x + -1.75) equal to 6.128825336 and -6.128825336.

Subproblem 1
x + -1.75 = 6.128825336

Simplifying
x + -1.75 = 6.128825336

Reorder the terms:
-1.75 + x = 6.128825336

Solving
-1.75 + x = 6.128825336

Solving for variable 'x'.

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

Add '1.75' to each side of the equation.
-1.75 + 1.75 + x = 6.128825336 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + x = 6.128825336 + 1.75
x = 6.128825336 + 1.75

Combine like terms: 6.128825336 + 1.75 = 7.878825336
x = 7.878825336

Simplifying
x = 7.878825336

Subproblem 2
x + -1.75 = -6.128825336

Simplifying
x + -1.75 = -6.128825336

Reorder the terms:
-1.75 + x = -6.128825336

Solving
-1.75 + x = -6.128825336

Solving for variable 'x'.

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

Add '1.75' to each side of the equation.
-1.75 + 1.75 + x = -6.128825336 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + x = -6.128825336 + 1.75
x = -6.128825336 + 1.75

Combine like terms: -6.128825336 + 1.75 = -4.378825336
x = -4.378825336

Simplifying
x = -4.378825336

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.878825336, -4.378825336}
Solution
x = {7.878825336, -4.378825336}