8.75=(x+2)(x+3)

Solution for 8.75=(x+2)(x+3) equation:

Simplifying
8.75 = (x + 2)(x + 3)

Reorder the terms:
8.75 = (2 + x)(x + 3)

Reorder the terms:
8.75 = (2 + x)(3 + x)

Multiply (2 + x) * (3 + x)
8.75 = (2(3 + x) + x(3 + x))
8.75 = ((3 * 2 + x * 2) + x(3 + x))
8.75 = ((6 + 2x) + x(3 + x))
8.75 = (6 + 2x + (3 * x + x * x))
8.75 = (6 + 2x + (3x + x2))

Combine like terms: 2x + 3x = 5x
8.75 = (6 + 5x + x2)

Solving
8.75 = 6 + 5x + x2

Solving for variable 'x'.

Combine like terms: 8.75 + -6 = 2.75
2.75 + -5x + -1x2 = 6 + 5x + x2 + -6 + -5x + -1x2

Reorder the terms:
2.75 + -5x + -1x2 = 6 + -6 + 5x + -5x + x2 + -1x2

Combine like terms: 6 + -6 = 0
2.75 + -5x + -1x2 = 0 + 5x + -5x + x2 + -1x2
2.75 + -5x + -1x2 = 5x + -5x + x2 + -1x2

Combine like terms: 5x + -5x = 0
2.75 + -5x + -1x2 = 0 + x2 + -1x2
2.75 + -5x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
2.75 + -5x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-2.75 + 5x + x2 = 0

Move the constant term to the right:

Add '2.75' to each side of the equation.
-2.75 + 5x + 2.75 + x2 = 0 + 2.75

Reorder the terms:
-2.75 + 2.75 + 5x + x2 = 0 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + 5x + x2 = 0 + 2.75
5x + x2 = 0 + 2.75

Combine like terms: 0 + 2.75 = 2.75
5x + x2 = 2.75

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 2.75 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 2.75 + 6.25

Combine like terms: 2.75 + 6.25 = 9
6.25 + 5x + x2 = 9

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 9

Calculate the square root of the right side: 3

Break this problem into two subproblems by setting 
(x + 2.5) equal to 3 and -3.

Subproblem 1
x + 2.5 = 3

Simplifying
x + 2.5 = 3

Reorder the terms:
2.5 + x = 3

Solving
2.5 + x = 3

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 3 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 3 + -2.5
x = 3 + -2.5

Combine like terms: 3 + -2.5 = 0.5
x = 0.5

Simplifying
x = 0.5

Subproblem 2
x + 2.5 = -3

Simplifying
x + 2.5 = -3

Reorder the terms:
2.5 + x = -3

Solving
2.5 + x = -3

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -3 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -3 + -2.5
x = -3 + -2.5

Combine like terms: -3 + -2.5 = -5.5
x = -5.5

Simplifying
x = -5.5

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.5, -5.5}