(5x^3-5x^2+8x)+(9x^3+9x^2-13x)=

Solution for (5x^3-5x^2+8x)+(9x^3+9x^2-13x)= equation:

Simplifying
(5x3 + -5x2 + 8x) + (9x3 + 9x2 + -13x) = 0

Reorder the terms:
(8x + -5x2 + 5x3) + (9x3 + 9x2 + -13x) = 0

Remove parenthesis around (8x + -5x2 + 5x3)
8x + -5x2 + 5x3 + (9x3 + 9x2 + -13x) = 0

Reorder the terms:
8x + -5x2 + 5x3 + (-13x + 9x2 + 9x3) = 0

Remove parenthesis around (-13x + 9x2 + 9x3)
8x + -5x2 + 5x3 + -13x + 9x2 + 9x3 = 0

Reorder the terms:
8x + -13x + -5x2 + 9x2 + 5x3 + 9x3 = 0

Combine like terms: 8x + -13x = -5x
-5x + -5x2 + 9x2 + 5x3 + 9x3 = 0

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

Combine like terms: 5x3 + 9x3 = 14x3
-5x + 4x2 + 14x3 = 0

Solving
-5x + 4x2 + 14x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-5 + 4x + 14x2) = 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 '(-5 + 4x + 14x2)' equal to zero and attempt to solve:

Simplifying
-5 + 4x + 14x2 = 0

Solving
-5 + 4x + 14x2 = 0

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

Divide each side by '14'.
-0.3571428571 + 0.2857142857x + x2 = 0

Move the constant term to the right:

Add '0.3571428571' to each side of the equation.
-0.3571428571 + 0.2857142857x + 0.3571428571 + x2 = 0 + 0.3571428571

Reorder the terms:
-0.3571428571 + 0.3571428571 + 0.2857142857x + x2 = 0 + 0.3571428571

Combine like terms: -0.3571428571 + 0.3571428571 = 0.0000000000
0.0000000000 + 0.2857142857x + x2 = 0 + 0.3571428571
0.2857142857x + x2 = 0 + 0.3571428571

Combine like terms: 0 + 0.3571428571 = 0.3571428571
0.2857142857x + x2 = 0.3571428571

The x term is 0.2857142857x.  Take half its coefficient (0.1428571429).
Square it (0.02040816328) and add it to both sides.

Add '0.02040816328' to each side of the equation.
0.2857142857x + 0.02040816328 + x2 = 0.3571428571 + 0.02040816328

Reorder the terms:
0.02040816328 + 0.2857142857x + x2 = 0.3571428571 + 0.02040816328

Combine like terms: 0.3571428571 + 0.02040816328 = 0.37755102038
0.02040816328 + 0.2857142857x + x2 = 0.37755102038

Factor a perfect square on the left side:
(x + 0.1428571429)(x + 0.1428571429) = 0.37755102038

Calculate the square root of the right side: 0.614451805

Break this problem into two subproblems by setting 
(x + 0.1428571429) equal to 0.614451805 and -0.614451805.

Subproblem 1
x + 0.1428571429 = 0.614451805

Simplifying
x + 0.1428571429 = 0.614451805

Reorder the terms:
0.1428571429 + x = 0.614451805

Solving
0.1428571429 + x = 0.614451805

Solving for variable 'x'.

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

Add '-0.1428571429' to each side of the equation.
0.1428571429 + -0.1428571429 + x = 0.614451805 + -0.1428571429

Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000
0.0000000000 + x = 0.614451805 + -0.1428571429
x = 0.614451805 + -0.1428571429

Combine like terms: 0.614451805 + -0.1428571429 = 0.4715946621
x = 0.4715946621

Simplifying
x = 0.4715946621

Subproblem 2
x + 0.1428571429 = -0.614451805

Simplifying
x + 0.1428571429 = -0.614451805

Reorder the terms:
0.1428571429 + x = -0.614451805

Solving
0.1428571429 + x = -0.614451805

Solving for variable 'x'.

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

Add '-0.1428571429' to each side of the equation.
0.1428571429 + -0.1428571429 + x = -0.614451805 + -0.1428571429

Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000
0.0000000000 + x = -0.614451805 + -0.1428571429
x = -0.614451805 + -0.1428571429

Combine like terms: -0.614451805 + -0.1428571429 = -0.7573089479
x = -0.7573089479

Simplifying
x = -0.7573089479

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.4715946621, -0.7573089479}
Solution
x = {0, 0.4715946621, -0.7573089479}