(9x^3-6x^2+7x)+(5x^3+8x^2-10x)=

Solution for (9x^3-6x^2+7x)+(5x^3+8x^2-10x)= equation:

Simplifying
(9x3 + -6x2 + 7x) + (5x3 + 8x2 + -10x) = 0

Reorder the terms:
(7x + -6x2 + 9x3) + (5x3 + 8x2 + -10x) = 0

Remove parenthesis around (7x + -6x2 + 9x3)
7x + -6x2 + 9x3 + (5x3 + 8x2 + -10x) = 0

Reorder the terms:
7x + -6x2 + 9x3 + (-10x + 8x2 + 5x3) = 0

Remove parenthesis around (-10x + 8x2 + 5x3)
7x + -6x2 + 9x3 + -10x + 8x2 + 5x3 = 0

Reorder the terms:
7x + -10x + -6x2 + 8x2 + 9x3 + 5x3 = 0

Combine like terms: 7x + -10x = -3x
-3x + -6x2 + 8x2 + 9x3 + 5x3 = 0

Combine like terms: -6x2 + 8x2 = 2x2
-3x + 2x2 + 9x3 + 5x3 = 0

Combine like terms: 9x3 + 5x3 = 14x3
-3x + 2x2 + 14x3 = 0

Solving
-3x + 2x2 + 14x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-3 + 2x + 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 '(-3 + 2x + 14x2)' equal to zero and attempt to solve:

Simplifying
-3 + 2x + 14x2 = 0

Solving
-3 + 2x + 14x2 = 0

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

Divide each side by '14'.
-0.2142857143 + 0.1428571429x + x2 = 0

Move the constant term to the right:

Add '0.2142857143' to each side of the equation.
-0.2142857143 + 0.1428571429x + 0.2142857143 + x2 = 0 + 0.2142857143

Reorder the terms:
-0.2142857143 + 0.2142857143 + 0.1428571429x + x2 = 0 + 0.2142857143

Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000
0.0000000000 + 0.1428571429x + x2 = 0 + 0.2142857143
0.1428571429x + x2 = 0 + 0.2142857143

Combine like terms: 0 + 0.2142857143 = 0.2142857143
0.1428571429x + x2 = 0.2142857143

The x term is 0.1428571429x.  Take half its coefficient (0.07142857145).
Square it (0.005102040819) and add it to both sides.

Add '0.005102040819' to each side of the equation.
0.1428571429x + 0.005102040819 + x2 = 0.2142857143 + 0.005102040819

Reorder the terms:
0.005102040819 + 0.1428571429x + x2 = 0.2142857143 + 0.005102040819

Combine like terms: 0.2142857143 + 0.005102040819 = 0.219387755119
0.005102040819 + 0.1428571429x + x2 = 0.219387755119

Factor a perfect square on the left side:
(x + 0.07142857145)(x + 0.07142857145) = 0.219387755119

Calculate the square root of the right side: 0.468388466

Break this problem into two subproblems by setting 
(x + 0.07142857145) equal to 0.468388466 and -0.468388466.

Subproblem 1
x + 0.07142857145 = 0.468388466

Simplifying
x + 0.07142857145 = 0.468388466

Reorder the terms:
0.07142857145 + x = 0.468388466

Solving
0.07142857145 + x = 0.468388466

Solving for variable 'x'.

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

Add '-0.07142857145' to each side of the equation.
0.07142857145 + -0.07142857145 + x = 0.468388466 + -0.07142857145

Combine like terms: 0.07142857145 + -0.07142857145 = 0.00000000000
0.00000000000 + x = 0.468388466 + -0.07142857145
x = 0.468388466 + -0.07142857145

Combine like terms: 0.468388466 + -0.07142857145 = 0.39695989455
x = 0.39695989455

Simplifying
x = 0.39695989455

Subproblem 2
x + 0.07142857145 = -0.468388466

Simplifying
x + 0.07142857145 = -0.468388466

Reorder the terms:
0.07142857145 + x = -0.468388466

Solving
0.07142857145 + x = -0.468388466

Solving for variable 'x'.

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

Add '-0.07142857145' to each side of the equation.
0.07142857145 + -0.07142857145 + x = -0.468388466 + -0.07142857145

Combine like terms: 0.07142857145 + -0.07142857145 = 0.00000000000
0.00000000000 + x = -0.468388466 + -0.07142857145
x = -0.468388466 + -0.07142857145

Combine like terms: -0.468388466 + -0.07142857145 = -0.53981703745
x = -0.53981703745

Simplifying
x = -0.53981703745

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.39695989455, -0.53981703745}
Solution
x = {0, 0.39695989455, -0.53981703745}