(x)(x-1)(24)=4568

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Solution for (x)(x-1)(24)=4568 equation: 


Simplifying
(x)(x + -1)(24) = 4568

Reorder the terms:
x(-1 + x)(24) = 4568

Reorder the terms for easier multiplication:
24x(-1 + x) = 4568
(-1 * 24x + x * 24x) = 4568
(-24x + 24x2) = 4568

Solving
-24x + 24x2 = 4568

Solving for variable 'x'.

Reorder the terms:
-4568 + -24x + 24x2 = 4568 + -4568

Combine like terms: 4568 + -4568 = 0
-4568 + -24x + 24x2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-571 + -3x + 3x2) = 0

Ignore the factor 8.

Subproblem 1
Set the factor '(-571 + -3x + 3x2)' equal to zero and attempt to solve:

Simplifying
-571 + -3x + 3x2 = 0

Solving
-571 + -3x + 3x2 = 0

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

Divide each side by '3'.
-190.3333333 + -1x + x2 = 0

Move the constant term to the right:

Add '190.3333333' to each side of the equation.
-190.3333333 + -1x + 190.3333333 + x2 = 0 + 190.3333333

Reorder the terms:
-190.3333333 + 190.3333333 + -1x + x2 = 0 + 190.3333333

Combine like terms: -190.3333333 + 190.3333333 = 0.0000000
0.0000000 + -1x + x2 = 0 + 190.3333333
-1x + x2 = 0 + 190.3333333

Combine like terms: 0 + 190.3333333 = 190.3333333
-1x + x2 = 190.3333333

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 190.3333333 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 190.3333333 + 0.25

Combine like terms: 190.3333333 + 0.25 = 190.5833333
0.25 + -1x + x2 = 190.5833333

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 190.5833333

Calculate the square root of the right side: 13.805192259

Break this problem into two subproblems by setting 
(x + -0.5) equal to 13.805192259 and -13.805192259.


Subproblem 1
x + -0.5 = 13.805192259

Simplifying
x + -0.5 = 13.805192259

Reorder the terms:
-0.5 + x = 13.805192259

Solving
-0.5 + x = 13.805192259

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = 13.805192259 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 13.805192259 + 0.5
x = 13.805192259 + 0.5

Combine like terms: 13.805192259 + 0.5 = 14.305192259
x = 14.305192259

Simplifying
x = 14.305192259


Subproblem 2
x + -0.5 = -13.805192259

Simplifying
x + -0.5 = -13.805192259

Reorder the terms:
-0.5 + x = -13.805192259

Solving
-0.5 + x = -13.805192259

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = -13.805192259 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -13.805192259 + 0.5
x = -13.805192259 + 0.5

Combine like terms: -13.805192259 + 0.5 = -13.305192259
x = -13.305192259

Simplifying
x = -13.305192259


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {14.305192259, -13.305192259}
Solution
x = {14.305192259, -13.305192259}

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