2300=(10x+8)(x+4)

Solution for 2300=(10x+8)(x+4) equation:

Simplifying
2300 = (10x + 8)(x + 4)

Reorder the terms:
2300 = (8 + 10x)(x + 4)

Reorder the terms:
2300 = (8 + 10x)(4 + x)

Multiply (8 + 10x) * (4 + x)
2300 = (8(4 + x) + 10x * (4 + x))
2300 = ((4 * 8 + x * 8) + 10x * (4 + x))
2300 = ((32 + 8x) + 10x * (4 + x))
2300 = (32 + 8x + (4 * 10x + x * 10x))
2300 = (32 + 8x + (40x + 10x2))

Combine like terms: 8x + 40x = 48x
2300 = (32 + 48x + 10x2)

Solving
2300 = 32 + 48x + 10x2

Solving for variable 'x'.

Combine like terms: 2300 + -32 = 2268
2268 + -48x + -10x2 = 32 + 48x + 10x2 + -32 + -48x + -10x2

Reorder the terms:
2268 + -48x + -10x2 = 32 + -32 + 48x + -48x + 10x2 + -10x2

Combine like terms: 32 + -32 = 0
2268 + -48x + -10x2 = 0 + 48x + -48x + 10x2 + -10x2
2268 + -48x + -10x2 = 48x + -48x + 10x2 + -10x2

Combine like terms: 48x + -48x = 0
2268 + -48x + -10x2 = 0 + 10x2 + -10x2
2268 + -48x + -10x2 = 10x2 + -10x2

Combine like terms: 10x2 + -10x2 = 0
2268 + -48x + -10x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(1134 + -24x + -5x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(1134 + -24x + -5x2)' equal to zero and attempt to solve:

Simplifying
1134 + -24x + -5x2 = 0

Solving
1134 + -24x + -5x2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
-226.8 + 4.8x + x2 = 0

Move the constant term to the right:

Add '226.8' to each side of the equation.
-226.8 + 4.8x + 226.8 + x2 = 0 + 226.8

Reorder the terms:
-226.8 + 226.8 + 4.8x + x2 = 0 + 226.8

Combine like terms: -226.8 + 226.8 = 0.0
0.0 + 4.8x + x2 = 0 + 226.8
4.8x + x2 = 0 + 226.8

Combine like terms: 0 + 226.8 = 226.8
4.8x + x2 = 226.8

The x term is 4.8x.  Take half its coefficient (2.4).
Square it (5.76) and add it to both sides.

Add '5.76' to each side of the equation.
4.8x + 5.76 + x2 = 226.8 + 5.76

Reorder the terms:
5.76 + 4.8x + x2 = 226.8 + 5.76

Combine like terms: 226.8 + 5.76 = 232.56
5.76 + 4.8x + x2 = 232.56

Factor a perfect square on the left side:
(x + 2.4)(x + 2.4) = 232.56

Calculate the square root of the right side: 15.249918033

Break this problem into two subproblems by setting 
(x + 2.4) equal to 15.249918033 and -15.249918033.

Subproblem 1
x + 2.4 = 15.249918033

Simplifying
x + 2.4 = 15.249918033

Reorder the terms:
2.4 + x = 15.249918033

Solving
2.4 + x = 15.249918033

Solving for variable 'x'.

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

Add '-2.4' to each side of the equation.
2.4 + -2.4 + x = 15.249918033 + -2.4

Combine like terms: 2.4 + -2.4 = 0.0
0.0 + x = 15.249918033 + -2.4
x = 15.249918033 + -2.4

Combine like terms: 15.249918033 + -2.4 = 12.849918033
x = 12.849918033

Simplifying
x = 12.849918033

Subproblem 2
x + 2.4 = -15.249918033

Simplifying
x + 2.4 = -15.249918033

Reorder the terms:
2.4 + x = -15.249918033

Solving
2.4 + x = -15.249918033

Solving for variable 'x'.

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

Add '-2.4' to each side of the equation.
2.4 + -2.4 + x = -15.249918033 + -2.4

Combine like terms: 2.4 + -2.4 = 0.0
0.0 + x = -15.249918033 + -2.4
x = -15.249918033 + -2.4

Combine like terms: -15.249918033 + -2.4 = -17.649918033
x = -17.649918033

Simplifying
x = -17.649918033

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.849918033, -17.649918033}
Solution
x = {12.849918033, -17.649918033}