(9x^3-7x^2+6x)+(4x^3+9x^2-13x)=

Solution for (9x^3-7x^2+6x)+(4x^3+9x^2-13x)= equation:

Simplifying
(9x3 + -7x2 + 6x) + (4x3 + 9x2 + -13x) = 0

Reorder the terms:
(6x + -7x2 + 9x3) + (4x3 + 9x2 + -13x) = 0

Remove parenthesis around (6x + -7x2 + 9x3)
6x + -7x2 + 9x3 + (4x3 + 9x2 + -13x) = 0

Reorder the terms:
6x + -7x2 + 9x3 + (-13x + 9x2 + 4x3) = 0

Remove parenthesis around (-13x + 9x2 + 4x3)
6x + -7x2 + 9x3 + -13x + 9x2 + 4x3 = 0

Reorder the terms:
6x + -13x + -7x2 + 9x2 + 9x3 + 4x3 = 0

Combine like terms: 6x + -13x = -7x
-7x + -7x2 + 9x2 + 9x3 + 4x3 = 0

Combine like terms: -7x2 + 9x2 = 2x2
-7x + 2x2 + 9x3 + 4x3 = 0

Combine like terms: 9x3 + 4x3 = 13x3
-7x + 2x2 + 13x3 = 0

Solving
-7x + 2x2 + 13x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-7 + 2x + 13x2) = 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 + 2x + 13x2)' equal to zero and attempt to solve:

Simplifying
-7 + 2x + 13x2 = 0

Solving
-7 + 2x + 13x2 = 0

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

Divide each side by '13'.
-0.5384615385 + 0.1538461538x + x2 = 0

Move the constant term to the right:

Add '0.5384615385' to each side of the equation.
-0.5384615385 + 0.1538461538x + 0.5384615385 + x2 = 0 + 0.5384615385

Reorder the terms:
-0.5384615385 + 0.5384615385 + 0.1538461538x + x2 = 0 + 0.5384615385

Combine like terms: -0.5384615385 + 0.5384615385 = 0.0000000000
0.0000000000 + 0.1538461538x + x2 = 0 + 0.5384615385
0.1538461538x + x2 = 0 + 0.5384615385

Combine like terms: 0 + 0.5384615385 = 0.5384615385
0.1538461538x + x2 = 0.5384615385

The x term is 0.1538461538x.  Take half its coefficient (0.0769230769).
Square it (0.005917159760) and add it to both sides.

Add '0.005917159760' to each side of the equation.
0.1538461538x + 0.005917159760 + x2 = 0.5384615385 + 0.005917159760

Reorder the terms:
0.005917159760 + 0.1538461538x + x2 = 0.5384615385 + 0.005917159760

Combine like terms: 0.5384615385 + 0.005917159760 = 0.54437869826
0.005917159760 + 0.1538461538x + x2 = 0.54437869826

Factor a perfect square on the left side:
(x + 0.0769230769)(x + 0.0769230769) = 0.54437869826

Calculate the square root of the right side: 0.737820234

Break this problem into two subproblems by setting 
(x + 0.0769230769) equal to 0.737820234 and -0.737820234.

Subproblem 1
x + 0.0769230769 = 0.737820234

Simplifying
x + 0.0769230769 = 0.737820234

Reorder the terms:
0.0769230769 + x = 0.737820234

Solving
0.0769230769 + x = 0.737820234

Solving for variable 'x'.

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

Add '-0.0769230769' to each side of the equation.
0.0769230769 + -0.0769230769 + x = 0.737820234 + -0.0769230769

Combine like terms: 0.0769230769 + -0.0769230769 = 0.0000000000
0.0000000000 + x = 0.737820234 + -0.0769230769
x = 0.737820234 + -0.0769230769

Combine like terms: 0.737820234 + -0.0769230769 = 0.6608971571
x = 0.6608971571

Simplifying
x = 0.6608971571

Subproblem 2
x + 0.0769230769 = -0.737820234

Simplifying
x + 0.0769230769 = -0.737820234

Reorder the terms:
0.0769230769 + x = -0.737820234

Solving
0.0769230769 + x = -0.737820234

Solving for variable 'x'.

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

Add '-0.0769230769' to each side of the equation.
0.0769230769 + -0.0769230769 + x = -0.737820234 + -0.0769230769

Combine like terms: 0.0769230769 + -0.0769230769 = 0.0000000000
0.0000000000 + x = -0.737820234 + -0.0769230769
x = -0.737820234 + -0.0769230769

Combine like terms: -0.737820234 + -0.0769230769 = -0.8147433109
x = -0.8147433109

Simplifying
x = -0.8147433109

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.6608971571, -0.8147433109}
Solution
x = {0, 0.6608971571, -0.8147433109}