x=24x^3-28x^2+8x

Solution for x=24x^3-28x^2+8x equation:

Simplifying
x = 24x3 + -28x2 + 8x

Reorder the terms:
x = 8x + -28x2 + 24x3

Solving
x = 8x + -28x2 + 24x3

Solving for variable 'x'.

Combine like terms: x + -8x = -7x
-7x + 28x2 + -24x3 = 8x + -28x2 + 24x3 + -8x + 28x2 + -24x3

Reorder the terms:
-7x + 28x2 + -24x3 = 8x + -8x + -28x2 + 28x2 + 24x3 + -24x3

Combine like terms: 8x + -8x = 0
-7x + 28x2 + -24x3 = 0 + -28x2 + 28x2 + 24x3 + -24x3
-7x + 28x2 + -24x3 = -28x2 + 28x2 + 24x3 + -24x3

Combine like terms: -28x2 + 28x2 = 0
-7x + 28x2 + -24x3 = 0 + 24x3 + -24x3
-7x + 28x2 + -24x3 = 24x3 + -24x3

Combine like terms: 24x3 + -24x3 = 0
-7x + 28x2 + -24x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-7 + 28x + -24x2) = 0

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 + 28x + -24x2)' equal to zero and attempt to solve:

Simplifying
-7 + 28x + -24x2 = 0

Solving
-7 + 28x + -24x2 = 0

Begin completing the square.  Divide all terms by
-24 the coefficient of the squared term: 

Divide each side by '-24'.
0.2916666667 + -1.166666667x + x2 = 0

Move the constant term to the right:

Add '-0.2916666667' to each side of the equation.
0.2916666667 + -1.166666667x + -0.2916666667 + x2 = 0 + -0.2916666667

Reorder the terms:
0.2916666667 + -0.2916666667 + -1.166666667x + x2 = 0 + -0.2916666667

Combine like terms: 0.2916666667 + -0.2916666667 = 0.0000000000
0.0000000000 + -1.166666667x + x2 = 0 + -0.2916666667
-1.166666667x + x2 = 0 + -0.2916666667

Combine like terms: 0 + -0.2916666667 = -0.2916666667
-1.166666667x + x2 = -0.2916666667

The x term is -1.166666667x.  Take half its coefficient (-0.5833333335).
Square it (0.3402777780) and add it to both sides.

Add '0.3402777780' to each side of the equation.
-1.166666667x + 0.3402777780 + x2 = -0.2916666667 + 0.3402777780

Reorder the terms:
0.3402777780 + -1.166666667x + x2 = -0.2916666667 + 0.3402777780

Combine like terms: -0.2916666667 + 0.3402777780 = 0.0486111113
0.3402777780 + -1.166666667x + x2 = 0.0486111113

Factor a perfect square on the left side:
(x + -0.5833333335)(x + -0.5833333335) = 0.0486111113

Calculate the square root of the right side: 0.220479276

Break this problem into two subproblems by setting 
(x + -0.5833333335) equal to 0.220479276 and -0.220479276.

Subproblem 1
x + -0.5833333335 = 0.220479276

Simplifying
x + -0.5833333335 = 0.220479276

Reorder the terms:
-0.5833333335 + x = 0.220479276

Solving
-0.5833333335 + x = 0.220479276

Solving for variable 'x'.

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

Add '0.5833333335' to each side of the equation.
-0.5833333335 + 0.5833333335 + x = 0.220479276 + 0.5833333335

Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000
0.0000000000 + x = 0.220479276 + 0.5833333335
x = 0.220479276 + 0.5833333335

Combine like terms: 0.220479276 + 0.5833333335 = 0.8038126095
x = 0.8038126095

Simplifying
x = 0.8038126095

Subproblem 2
x + -0.5833333335 = -0.220479276

Simplifying
x + -0.5833333335 = -0.220479276

Reorder the terms:
-0.5833333335 + x = -0.220479276

Solving
-0.5833333335 + x = -0.220479276

Solving for variable 'x'.

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

Add '0.5833333335' to each side of the equation.
-0.5833333335 + 0.5833333335 + x = -0.220479276 + 0.5833333335

Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000
0.0000000000 + x = -0.220479276 + 0.5833333335
x = -0.220479276 + 0.5833333335

Combine like terms: -0.220479276 + 0.5833333335 = 0.3628540575
x = 0.3628540575

Simplifying
x = 0.3628540575

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.8038126095, 0.3628540575}
Solution
x = {0, 0.8038126095, 0.3628540575}