(2x-5)(x+7)=180

Solution for (2x-5)(x+7)=180 equation:

Simplifying
(2x + -5)(x + 7) = 180

Reorder the terms:
(-5 + 2x)(x + 7) = 180

Reorder the terms:
(-5 + 2x)(7 + x) = 180

Multiply (-5 + 2x) * (7 + x)
(-5(7 + x) + 2x * (7 + x)) = 180
((7 * -5 + x * -5) + 2x * (7 + x)) = 180
((-35 + -5x) + 2x * (7 + x)) = 180
(-35 + -5x + (7 * 2x + x * 2x)) = 180
(-35 + -5x + (14x + 2x2)) = 180

Combine like terms: -5x + 14x = 9x
(-35 + 9x + 2x2) = 180

Solving
-35 + 9x + 2x2 = 180

Solving for variable 'x'.

Reorder the terms:
-35 + -180 + 9x + 2x2 = 180 + -180

Combine like terms: -35 + -180 = -215
-215 + 9x + 2x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-215 + 9x + 2x2 = 0

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

Divide each side by '2'.
-107.5 + 4.5x + x2 = 0

Move the constant term to the right:

Add '107.5' to each side of the equation.
-107.5 + 4.5x + 107.5 + x2 = 0 + 107.5

Reorder the terms:
-107.5 + 107.5 + 4.5x + x2 = 0 + 107.5

Combine like terms: -107.5 + 107.5 = 0.0
0.0 + 4.5x + x2 = 0 + 107.5
4.5x + x2 = 0 + 107.5

Combine like terms: 0 + 107.5 = 107.5
4.5x + x2 = 107.5

The x term is 4.5x.  Take half its coefficient (2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
4.5x + 5.0625 + x2 = 107.5 + 5.0625

Reorder the terms:
5.0625 + 4.5x + x2 = 107.5 + 5.0625

Combine like terms: 107.5 + 5.0625 = 112.5625
5.0625 + 4.5x + x2 = 112.5625

Factor a perfect square on the left side:
(x + 2.25)(x + 2.25) = 112.5625

Calculate the square root of the right side: 10.609547587

Break this problem into two subproblems by setting 
(x + 2.25) equal to 10.609547587 and -10.609547587.

Subproblem 1
x + 2.25 = 10.609547587

Simplifying
x + 2.25 = 10.609547587

Reorder the terms:
2.25 + x = 10.609547587

Solving
2.25 + x = 10.609547587

Solving for variable 'x'.

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

Add '-2.25' to each side of the equation.
2.25 + -2.25 + x = 10.609547587 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + x = 10.609547587 + -2.25
x = 10.609547587 + -2.25

Combine like terms: 10.609547587 + -2.25 = 8.359547587
x = 8.359547587

Simplifying
x = 8.359547587

Subproblem 2
x + 2.25 = -10.609547587

Simplifying
x + 2.25 = -10.609547587

Reorder the terms:
2.25 + x = -10.609547587

Solving
2.25 + x = -10.609547587

Solving for variable 'x'.

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

Add '-2.25' to each side of the equation.
2.25 + -2.25 + x = -10.609547587 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + x = -10.609547587 + -2.25
x = -10.609547587 + -2.25

Combine like terms: -10.609547587 + -2.25 = -12.859547587
x = -12.859547587

Simplifying
x = -12.859547587

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.359547587, -12.859547587}