0=3x^3-11x^2+4x

Solution for 0=3x^3-11x^2+4x equation:

Simplifying
0 = 3x3 + -11x2 + 4x

Reorder the terms:
0 = 4x + -11x2 + 3x3

Solving
0 = 4x + -11x2 + 3x3

Solving for variable 'x'.
Remove the zero:
-4x + 11x2 + -3x3 = 4x + -11x2 + 3x3 + -4x + 11x2 + -3x3

Reorder the terms:
-4x + 11x2 + -3x3 = 4x + -4x + -11x2 + 11x2 + 3x3 + -3x3

Combine like terms: 4x + -4x = 0
-4x + 11x2 + -3x3 = 0 + -11x2 + 11x2 + 3x3 + -3x3
-4x + 11x2 + -3x3 = -11x2 + 11x2 + 3x3 + -3x3

Combine like terms: -11x2 + 11x2 = 0
-4x + 11x2 + -3x3 = 0 + 3x3 + -3x3
-4x + 11x2 + -3x3 = 3x3 + -3x3

Combine like terms: 3x3 + -3x3 = 0
-4x + 11x2 + -3x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-4 + 11x + -3x2) = 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 '(-4 + 11x + -3x2)' equal to zero and attempt to solve:

Simplifying
-4 + 11x + -3x2 = 0

Solving
-4 + 11x + -3x2 = 0

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

Divide each side by '-3'.
1.333333333 + -3.666666667x + x2 = 0

Move the constant term to the right:

Add '-1.333333333' to each side of the equation.
1.333333333 + -3.666666667x + -1.333333333 + x2 = 0 + -1.333333333

Reorder the terms:
1.333333333 + -1.333333333 + -3.666666667x + x2 = 0 + -1.333333333

Combine like terms: 1.333333333 + -1.333333333 = 0.000000000
0.000000000 + -3.666666667x + x2 = 0 + -1.333333333
-3.666666667x + x2 = 0 + -1.333333333

Combine like terms: 0 + -1.333333333 = -1.333333333
-3.666666667x + x2 = -1.333333333

The x term is -3.666666667x.  Take half its coefficient (-1.833333334).
Square it (3.361111114) and add it to both sides.

Add '3.361111114' to each side of the equation.
-3.666666667x + 3.361111114 + x2 = -1.333333333 + 3.361111114

Reorder the terms:
3.361111114 + -3.666666667x + x2 = -1.333333333 + 3.361111114

Combine like terms: -1.333333333 + 3.361111114 = 2.027777781
3.361111114 + -3.666666667x + x2 = 2.027777781

Factor a perfect square on the left side:
(x + -1.833333334)(x + -1.833333334) = 2.027777781

Calculate the square root of the right side: 1.424000625

Break this problem into two subproblems by setting 
(x + -1.833333334) equal to 1.424000625 and -1.424000625.

Subproblem 1
x + -1.833333334 = 1.424000625

Simplifying
x + -1.833333334 = 1.424000625

Reorder the terms:
-1.833333334 + x = 1.424000625

Solving
-1.833333334 + x = 1.424000625

Solving for variable 'x'.

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

Add '1.833333334' to each side of the equation.
-1.833333334 + 1.833333334 + x = 1.424000625 + 1.833333334

Combine like terms: -1.833333334 + 1.833333334 = 0.000000000
0.000000000 + x = 1.424000625 + 1.833333334
x = 1.424000625 + 1.833333334

Combine like terms: 1.424000625 + 1.833333334 = 3.257333959
x = 3.257333959

Simplifying
x = 3.257333959

Subproblem 2
x + -1.833333334 = -1.424000625

Simplifying
x + -1.833333334 = -1.424000625

Reorder the terms:
-1.833333334 + x = -1.424000625

Solving
-1.833333334 + x = -1.424000625

Solving for variable 'x'.

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

Add '1.833333334' to each side of the equation.
-1.833333334 + 1.833333334 + x = -1.424000625 + 1.833333334

Combine like terms: -1.833333334 + 1.833333334 = 0.000000000
0.000000000 + x = -1.424000625 + 1.833333334
x = -1.424000625 + 1.833333334

Combine like terms: -1.424000625 + 1.833333334 = 0.409332709
x = 0.409332709

Simplifying
x = 0.409332709

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.257333959, 0.409332709}
Solution
x = {0, 3.257333959, 0.409332709}