4x(3x-1)=24

Solution for 4x(3x-1)=24 equation:

Simplifying
4x(3x + -1) = 24

Reorder the terms:
4x(-1 + 3x) = 24
(-1 * 4x + 3x * 4x) = 24
(-4x + 12x2) = 24

Solving
-4x + 12x2 = 24

Solving for variable 'x'.

Reorder the terms:
-24 + -4x + 12x2 = 24 + -24

Combine like terms: 24 + -24 = 0
-24 + -4x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-6 + -1x + 3x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-6 + -1x + 3x2)' equal to zero and attempt to solve:

Simplifying
-6 + -1x + 3x2 = 0

Solving
-6 + -1x + 3x2 = 0

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

Divide each side by '3'.
-2 + -0.3333333333x + x2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -0.3333333333x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + -0.3333333333x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -0.3333333333x + x2 = 0 + 2
-0.3333333333x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
-0.3333333333x + x2 = 2

The x term is -0.3333333333x.  Take half its coefficient (-0.1666666667).
Square it (0.02777777779) and add it to both sides.

Add '0.02777777779' to each side of the equation.
-0.3333333333x + 0.02777777779 + x2 = 2 + 0.02777777779

Reorder the terms:
0.02777777779 + -0.3333333333x + x2 = 2 + 0.02777777779

Combine like terms: 2 + 0.02777777779 = 2.02777777779
0.02777777779 + -0.3333333333x + x2 = 2.02777777779

Factor a perfect square on the left side:
(x + -0.1666666667)(x + -0.1666666667) = 2.02777777779

Calculate the square root of the right side: 1.424000624

Break this problem into two subproblems by setting 
(x + -0.1666666667) equal to 1.424000624 and -1.424000624.

Subproblem 1
x + -0.1666666667 = 1.424000624

Simplifying
x + -0.1666666667 = 1.424000624

Reorder the terms:
-0.1666666667 + x = 1.424000624

Solving
-0.1666666667 + x = 1.424000624

Solving for variable 'x'.

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

Add '0.1666666667' to each side of the equation.
-0.1666666667 + 0.1666666667 + x = 1.424000624 + 0.1666666667

Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000
0.0000000000 + x = 1.424000624 + 0.1666666667
x = 1.424000624 + 0.1666666667

Combine like terms: 1.424000624 + 0.1666666667 = 1.5906672907
x = 1.5906672907

Simplifying
x = 1.5906672907

Subproblem 2
x + -0.1666666667 = -1.424000624

Simplifying
x + -0.1666666667 = -1.424000624

Reorder the terms:
-0.1666666667 + x = -1.424000624

Solving
-0.1666666667 + x = -1.424000624

Solving for variable 'x'.

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

Add '0.1666666667' to each side of the equation.
-0.1666666667 + 0.1666666667 + x = -1.424000624 + 0.1666666667

Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000
0.0000000000 + x = -1.424000624 + 0.1666666667
x = -1.424000624 + 0.1666666667

Combine like terms: -1.424000624 + 0.1666666667 = -1.2573339573
x = -1.2573339573

Simplifying
x = -1.2573339573

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.5906672907, -1.2573339573}
Solution
x = {1.5906672907, -1.2573339573}