(3x^3-3x^2+3x)+(9x^3+5x^2-14x)=

Solution for (3x^3-3x^2+3x)+(9x^3+5x^2-14x)= equation:

Simplifying
(3x3 + -3x2 + 3x) + (9x3 + 5x2 + -14x) = 0

Reorder the terms:
(3x + -3x2 + 3x3) + (9x3 + 5x2 + -14x) = 0

Remove parenthesis around (3x + -3x2 + 3x3)
3x + -3x2 + 3x3 + (9x3 + 5x2 + -14x) = 0

Reorder the terms:
3x + -3x2 + 3x3 + (-14x + 5x2 + 9x3) = 0

Remove parenthesis around (-14x + 5x2 + 9x3)
3x + -3x2 + 3x3 + -14x + 5x2 + 9x3 = 0

Reorder the terms:
3x + -14x + -3x2 + 5x2 + 3x3 + 9x3 = 0

Combine like terms: 3x + -14x = -11x
-11x + -3x2 + 5x2 + 3x3 + 9x3 = 0

Combine like terms: -3x2 + 5x2 = 2x2
-11x + 2x2 + 3x3 + 9x3 = 0

Combine like terms: 3x3 + 9x3 = 12x3
-11x + 2x2 + 12x3 = 0

Solving
-11x + 2x2 + 12x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-11 + 2x + 12x2) = 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 '(-11 + 2x + 12x2)' equal to zero and attempt to solve:

Simplifying
-11 + 2x + 12x2 = 0

Solving
-11 + 2x + 12x2 = 0

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

Divide each side by '12'.
-0.9166666667 + 0.1666666667x + x2 = 0

Move the constant term to the right:

Add '0.9166666667' to each side of the equation.
-0.9166666667 + 0.1666666667x + 0.9166666667 + x2 = 0 + 0.9166666667

Reorder the terms:
-0.9166666667 + 0.9166666667 + 0.1666666667x + x2 = 0 + 0.9166666667

Combine like terms: -0.9166666667 + 0.9166666667 = 0.0000000000
0.0000000000 + 0.1666666667x + x2 = 0 + 0.9166666667
0.1666666667x + x2 = 0 + 0.9166666667

Combine like terms: 0 + 0.9166666667 = 0.9166666667
0.1666666667x + x2 = 0.9166666667

The x term is 0.1666666667x.  Take half its coefficient (0.08333333335).
Square it (0.006944444447) and add it to both sides.

Add '0.006944444447' to each side of the equation.
0.1666666667x + 0.006944444447 + x2 = 0.9166666667 + 0.006944444447

Reorder the terms:
0.006944444447 + 0.1666666667x + x2 = 0.9166666667 + 0.006944444447

Combine like terms: 0.9166666667 + 0.006944444447 = 0.923611111147
0.006944444447 + 0.1666666667x + x2 = 0.923611111147

Factor a perfect square on the left side:
(x + 0.08333333335)(x + 0.08333333335) = 0.923611111147

Calculate the square root of the right side: 0.961046883

Break this problem into two subproblems by setting 
(x + 0.08333333335) equal to 0.961046883 and -0.961046883.

Subproblem 1
x + 0.08333333335 = 0.961046883

Simplifying
x + 0.08333333335 = 0.961046883

Reorder the terms:
0.08333333335 + x = 0.961046883

Solving
0.08333333335 + x = 0.961046883

Solving for variable 'x'.

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

Add '-0.08333333335' to each side of the equation.
0.08333333335 + -0.08333333335 + x = 0.961046883 + -0.08333333335

Combine like terms: 0.08333333335 + -0.08333333335 = 0.00000000000
0.00000000000 + x = 0.961046883 + -0.08333333335
x = 0.961046883 + -0.08333333335

Combine like terms: 0.961046883 + -0.08333333335 = 0.87771354965
x = 0.87771354965

Simplifying
x = 0.87771354965

Subproblem 2
x + 0.08333333335 = -0.961046883

Simplifying
x + 0.08333333335 = -0.961046883

Reorder the terms:
0.08333333335 + x = -0.961046883

Solving
0.08333333335 + x = -0.961046883

Solving for variable 'x'.

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

Add '-0.08333333335' to each side of the equation.
0.08333333335 + -0.08333333335 + x = -0.961046883 + -0.08333333335

Combine like terms: 0.08333333335 + -0.08333333335 = 0.00000000000
0.00000000000 + x = -0.961046883 + -0.08333333335
x = -0.961046883 + -0.08333333335

Combine like terms: -0.961046883 + -0.08333333335 = -1.04438021635
x = -1.04438021635

Simplifying
x = -1.04438021635

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.87771354965, -1.04438021635}
Solution
x = {0, 0.87771354965, -1.04438021635}