24x^3-44x^2+28x=0

Solution for 24x^3-44x^2+28x=0 equation:

Simplifying
24x3 + -44x2 + 28x = 0

Reorder the terms:
28x + -44x2 + 24x3 = 0

Solving
28x + -44x2 + 24x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x'.
4x(7 + -11x + 6x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(7 + -11x + 6x2)' equal to zero and attempt to solve:

Simplifying
7 + -11x + 6x2 = 0

Solving
7 + -11x + 6x2 = 0

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

Divide each side by '6'.
1.166666667 + -1.833333333x + x2 = 0

Move the constant term to the right:

Add '-1.166666667' to each side of the equation.
1.166666667 + -1.833333333x + -1.166666667 + x2 = 0 + -1.166666667

Reorder the terms:
1.166666667 + -1.166666667 + -1.833333333x + x2 = 0 + -1.166666667

Combine like terms: 1.166666667 + -1.166666667 = 0.000000000
0.000000000 + -1.833333333x + x2 = 0 + -1.166666667
-1.833333333x + x2 = 0 + -1.166666667

Combine like terms: 0 + -1.166666667 = -1.166666667
-1.833333333x + x2 = -1.166666667

The x term is -1.833333333x.  Take half its coefficient (-0.9166666665).
Square it (0.8402777775) and add it to both sides.

Add '0.8402777775' to each side of the equation.
-1.833333333x + 0.8402777775 + x2 = -1.166666667 + 0.8402777775

Reorder the terms:
0.8402777775 + -1.833333333x + x2 = -1.166666667 + 0.8402777775

Combine like terms: -1.166666667 + 0.8402777775 = -0.3263888895
0.8402777775 + -1.833333333x + x2 = -0.3263888895

Factor a perfect square on the left side:
(x + -0.9166666665)(x + -0.9166666665) = -0.3263888895

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}