7.5=(5-2x)(7+x)

Solution for 7.5=(5-2x)(7+x) equation:

Simplifying
7.5 = (5 + -2x)(7 + x)

Multiply (5 + -2x) * (7 + x)
7.5 = (5(7 + x) + -2x * (7 + x))
7.5 = ((7 * 5 + x * 5) + -2x * (7 + x))
7.5 = ((35 + 5x) + -2x * (7 + x))
7.5 = (35 + 5x + (7 * -2x + x * -2x))
7.5 = (35 + 5x + (-14x + -2x2))

Combine like terms: 5x + -14x = -9x
7.5 = (35 + -9x + -2x2)

Solving
7.5 = 35 + -9x + -2x2

Solving for variable 'x'.

Combine like terms: 7.5 + -35 = -27.5
-27.5 + 9x + 2x2 = 35 + -9x + -2x2 + -35 + 9x + 2x2

Reorder the terms:
-27.5 + 9x + 2x2 = 35 + -35 + -9x + 9x + -2x2 + 2x2

Combine like terms: 35 + -35 = 0
-27.5 + 9x + 2x2 = 0 + -9x + 9x + -2x2 + 2x2
-27.5 + 9x + 2x2 = -9x + 9x + -2x2 + 2x2

Combine like terms: -9x + 9x = 0
-27.5 + 9x + 2x2 = 0 + -2x2 + 2x2
-27.5 + 9x + 2x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
-27.5 + 9x + 2x2 = 0

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

Divide each side by '2'.
-13.75 + 4.5x + x2 = 0

Move the constant term to the right:

Add '13.75' to each side of the equation.
-13.75 + 4.5x + 13.75 + x2 = 0 + 13.75

Reorder the terms:
-13.75 + 13.75 + 4.5x + x2 = 0 + 13.75

Combine like terms: -13.75 + 13.75 = 0.00
0.00 + 4.5x + x2 = 0 + 13.75
4.5x + x2 = 0 + 13.75

Combine like terms: 0 + 13.75 = 13.75
4.5x + x2 = 13.75

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 = 13.75 + 5.0625

Reorder the terms:
5.0625 + 4.5x + x2 = 13.75 + 5.0625

Combine like terms: 13.75 + 5.0625 = 18.8125
5.0625 + 4.5x + x2 = 18.8125

Factor a perfect square on the left side:
(x + 2.25)(x + 2.25) = 18.8125

Calculate the square root of the right side: 4.337337893

Break this problem into two subproblems by setting 
(x + 2.25) equal to 4.337337893 and -4.337337893.

Subproblem 1
x + 2.25 = 4.337337893

Simplifying
x + 2.25 = 4.337337893

Reorder the terms:
2.25 + x = 4.337337893

Solving
2.25 + x = 4.337337893

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 = 4.337337893 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + x = 4.337337893 + -2.25
x = 4.337337893 + -2.25

Combine like terms: 4.337337893 + -2.25 = 2.087337893
x = 2.087337893

Simplifying
x = 2.087337893

Subproblem 2
x + 2.25 = -4.337337893

Simplifying
x + 2.25 = -4.337337893

Reorder the terms:
2.25 + x = -4.337337893

Solving
2.25 + x = -4.337337893

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 = -4.337337893 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + x = -4.337337893 + -2.25
x = -4.337337893 + -2.25

Combine like terms: -4.337337893 + -2.25 = -6.587337893
x = -6.587337893

Simplifying
x = -6.587337893

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.087337893, -6.587337893}