(2x-5)(x+5)=75

Solution for (2x-5)(x+5)=75 equation:

Simplifying
(2x + -5)(x + 5) = 75

Reorder the terms:
(-5 + 2x)(x + 5) = 75

Reorder the terms:
(-5 + 2x)(5 + x) = 75

Multiply (-5 + 2x) * (5 + x)
(-5(5 + x) + 2x * (5 + x)) = 75
((5 * -5 + x * -5) + 2x * (5 + x)) = 75
((-25 + -5x) + 2x * (5 + x)) = 75
(-25 + -5x + (5 * 2x + x * 2x)) = 75
(-25 + -5x + (10x + 2x2)) = 75

Combine like terms: -5x + 10x = 5x
(-25 + 5x + 2x2) = 75

Solving
-25 + 5x + 2x2 = 75

Solving for variable 'x'.

Reorder the terms:
-25 + -75 + 5x + 2x2 = 75 + -75

Combine like terms: -25 + -75 = -100
-100 + 5x + 2x2 = 75 + -75

Combine like terms: 75 + -75 = 0
-100 + 5x + 2x2 = 0

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

Divide each side by '2'.
-50 + 2.5x + x2 = 0

Move the constant term to the right:

Add '50' to each side of the equation.
-50 + 2.5x + 50 + x2 = 0 + 50

Reorder the terms:
-50 + 50 + 2.5x + x2 = 0 + 50

Combine like terms: -50 + 50 = 0
0 + 2.5x + x2 = 0 + 50
2.5x + x2 = 0 + 50

Combine like terms: 0 + 50 = 50
2.5x + x2 = 50

The x term is 2.5x.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5x + 1.5625 + x2 = 50 + 1.5625

Reorder the terms:
1.5625 + 2.5x + x2 = 50 + 1.5625

Combine like terms: 50 + 1.5625 = 51.5625
1.5625 + 2.5x + x2 = 51.5625

Factor a perfect square on the left side:
(x + 1.25)(x + 1.25) = 51.5625

Calculate the square root of the right side: 7.180703308

Break this problem into two subproblems by setting 
(x + 1.25) equal to 7.180703308 and -7.180703308.

Subproblem 1
x + 1.25 = 7.180703308

Simplifying
x + 1.25 = 7.180703308

Reorder the terms:
1.25 + x = 7.180703308

Solving
1.25 + x = 7.180703308

Solving for variable 'x'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + x = 7.180703308 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = 7.180703308 + -1.25
x = 7.180703308 + -1.25

Combine like terms: 7.180703308 + -1.25 = 5.930703308
x = 5.930703308

Simplifying
x = 5.930703308

Subproblem 2
x + 1.25 = -7.180703308

Simplifying
x + 1.25 = -7.180703308

Reorder the terms:
1.25 + x = -7.180703308

Solving
1.25 + x = -7.180703308

Solving for variable 'x'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + x = -7.180703308 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = -7.180703308 + -1.25
x = -7.180703308 + -1.25

Combine like terms: -7.180703308 + -1.25 = -8.430703308
x = -8.430703308

Simplifying
x = -8.430703308

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.930703308, -8.430703308}