(3x^3-5x^2+3x)+(4x^3+9x^2-11x)=

Solution for (3x^3-5x^2+3x)+(4x^3+9x^2-11x)= equation:

Simplifying
(3x3 + -5x2 + 3x) + (4x3 + 9x2 + -11x) = 0

Reorder the terms:
(3x + -5x2 + 3x3) + (4x3 + 9x2 + -11x) = 0

Remove parenthesis around (3x + -5x2 + 3x3)
3x + -5x2 + 3x3 + (4x3 + 9x2 + -11x) = 0

Reorder the terms:
3x + -5x2 + 3x3 + (-11x + 9x2 + 4x3) = 0

Remove parenthesis around (-11x + 9x2 + 4x3)
3x + -5x2 + 3x3 + -11x + 9x2 + 4x3 = 0

Reorder the terms:
3x + -11x + -5x2 + 9x2 + 3x3 + 4x3 = 0

Combine like terms: 3x + -11x = -8x
-8x + -5x2 + 9x2 + 3x3 + 4x3 = 0

Combine like terms: -5x2 + 9x2 = 4x2
-8x + 4x2 + 3x3 + 4x3 = 0

Combine like terms: 3x3 + 4x3 = 7x3
-8x + 4x2 + 7x3 = 0

Solving
-8x + 4x2 + 7x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-8 + 4x + 7x2) = 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 '(-8 + 4x + 7x2)' equal to zero and attempt to solve:

Simplifying
-8 + 4x + 7x2 = 0

Solving
-8 + 4x + 7x2 = 0

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

Divide each side by '7'.
-1.142857143 + 0.5714285714x + x2 = 0

Move the constant term to the right:

Add '1.142857143' to each side of the equation.
-1.142857143 + 0.5714285714x + 1.142857143 + x2 = 0 + 1.142857143

Reorder the terms:
-1.142857143 + 1.142857143 + 0.5714285714x + x2 = 0 + 1.142857143

Combine like terms: -1.142857143 + 1.142857143 = 0.000000000
0.000000000 + 0.5714285714x + x2 = 0 + 1.142857143
0.5714285714x + x2 = 0 + 1.142857143

Combine like terms: 0 + 1.142857143 = 1.142857143
0.5714285714x + x2 = 1.142857143

The x term is 0.5714285714x.  Take half its coefficient (0.2857142857).
Square it (0.08163265305) and add it to both sides.

Add '0.08163265305' to each side of the equation.
0.5714285714x + 0.08163265305 + x2 = 1.142857143 + 0.08163265305

Reorder the terms:
0.08163265305 + 0.5714285714x + x2 = 1.142857143 + 0.08163265305

Combine like terms: 1.142857143 + 0.08163265305 = 1.22448979605
0.08163265305 + 0.5714285714x + x2 = 1.22448979605

Factor a perfect square on the left side:
(x + 0.2857142857)(x + 0.2857142857) = 1.22448979605

Calculate the square root of the right side: 1.10656667

Break this problem into two subproblems by setting 
(x + 0.2857142857) equal to 1.10656667 and -1.10656667.

Subproblem 1
x + 0.2857142857 = 1.10656667

Simplifying
x + 0.2857142857 = 1.10656667

Reorder the terms:
0.2857142857 + x = 1.10656667

Solving
0.2857142857 + x = 1.10656667

Solving for variable 'x'.

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

Add '-0.2857142857' to each side of the equation.
0.2857142857 + -0.2857142857 + x = 1.10656667 + -0.2857142857

Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000
0.0000000000 + x = 1.10656667 + -0.2857142857
x = 1.10656667 + -0.2857142857

Combine like terms: 1.10656667 + -0.2857142857 = 0.8208523843
x = 0.8208523843

Simplifying
x = 0.8208523843

Subproblem 2
x + 0.2857142857 = -1.10656667

Simplifying
x + 0.2857142857 = -1.10656667

Reorder the terms:
0.2857142857 + x = -1.10656667

Solving
0.2857142857 + x = -1.10656667

Solving for variable 'x'.

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

Add '-0.2857142857' to each side of the equation.
0.2857142857 + -0.2857142857 + x = -1.10656667 + -0.2857142857

Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000
0.0000000000 + x = -1.10656667 + -0.2857142857
x = -1.10656667 + -0.2857142857

Combine like terms: -1.10656667 + -0.2857142857 = -1.3922809557
x = -1.3922809557

Simplifying
x = -1.3922809557

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.8208523843, -1.3922809557}
Solution
x = {0, 0.8208523843, -1.3922809557}