4368=(24+x)(x+1)

Solution for 4368=(24+x)(x+1) equation:

Simplifying
4368 = (24 + x)(x + 1)

Reorder the terms:
4368 = (24 + x)(1 + x)

Multiply (24 + x) * (1 + x)
4368 = (24(1 + x) + x(1 + x))
4368 = ((1 * 24 + x * 24) + x(1 + x))
4368 = ((24 + 24x) + x(1 + x))
4368 = (24 + 24x + (1 * x + x * x))
4368 = (24 + 24x + (1x + x2))

Combine like terms: 24x + 1x = 25x
4368 = (24 + 25x + x2)

Solving
4368 = 24 + 25x + x2

Solving for variable 'x'.

Combine like terms: 4368 + -24 = 4344
4344 + -25x + -1x2 = 24 + 25x + x2 + -24 + -25x + -1x2

Reorder the terms:
4344 + -25x + -1x2 = 24 + -24 + 25x + -25x + x2 + -1x2

Combine like terms: 24 + -24 = 0
4344 + -25x + -1x2 = 0 + 25x + -25x + x2 + -1x2
4344 + -25x + -1x2 = 25x + -25x + x2 + -1x2

Combine like terms: 25x + -25x = 0
4344 + -25x + -1x2 = 0 + x2 + -1x2
4344 + -25x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
4344 + -25x + -1x2 = 0

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

Divide each side by '-1'.
-4344 + 25x + x2 = 0

Move the constant term to the right:

Add '4344' to each side of the equation.
-4344 + 25x + 4344 + x2 = 0 + 4344

Reorder the terms:
-4344 + 4344 + 25x + x2 = 0 + 4344

Combine like terms: -4344 + 4344 = 0
0 + 25x + x2 = 0 + 4344
25x + x2 = 0 + 4344

Combine like terms: 0 + 4344 = 4344
25x + x2 = 4344

The x term is 25x.  Take half its coefficient (12.5).
Square it (156.25) and add it to both sides.

Add '156.25' to each side of the equation.
25x + 156.25 + x2 = 4344 + 156.25

Reorder the terms:
156.25 + 25x + x2 = 4344 + 156.25

Combine like terms: 4344 + 156.25 = 4500.25
156.25 + 25x + x2 = 4500.25

Factor a perfect square on the left side:
(x + 12.5)(x + 12.5) = 4500.25

Calculate the square root of the right side: 67.083902689

Break this problem into two subproblems by setting 
(x + 12.5) equal to 67.083902689 and -67.083902689.

Subproblem 1
x + 12.5 = 67.083902689

Simplifying
x + 12.5 = 67.083902689

Reorder the terms:
12.5 + x = 67.083902689

Solving
12.5 + x = 67.083902689

Solving for variable 'x'.

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

Add '-12.5' to each side of the equation.
12.5 + -12.5 + x = 67.083902689 + -12.5

Combine like terms: 12.5 + -12.5 = 0.0
0.0 + x = 67.083902689 + -12.5
x = 67.083902689 + -12.5

Combine like terms: 67.083902689 + -12.5 = 54.583902689
x = 54.583902689

Simplifying
x = 54.583902689

Subproblem 2
x + 12.5 = -67.083902689

Simplifying
x + 12.5 = -67.083902689

Reorder the terms:
12.5 + x = -67.083902689

Solving
12.5 + x = -67.083902689

Solving for variable 'x'.

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

Add '-12.5' to each side of the equation.
12.5 + -12.5 + x = -67.083902689 + -12.5

Combine like terms: 12.5 + -12.5 = 0.0
0.0 + x = -67.083902689 + -12.5
x = -67.083902689 + -12.5

Combine like terms: -67.083902689 + -12.5 = -79.583902689
x = -79.583902689

Simplifying
x = -79.583902689

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {54.583902689, -79.583902689}