(8x^3-7x^2+6x)+(3x^3+9x^2-14x)=

Solution for (8x^3-7x^2+6x)+(3x^3+9x^2-14x)= equation:

Simplifying
(8x3 + -7x2 + 6x) + (3x3 + 9x2 + -14x) = 0

Reorder the terms:
(6x + -7x2 + 8x3) + (3x3 + 9x2 + -14x) = 0

Remove parenthesis around (6x + -7x2 + 8x3)
6x + -7x2 + 8x3 + (3x3 + 9x2 + -14x) = 0

Reorder the terms:
6x + -7x2 + 8x3 + (-14x + 9x2 + 3x3) = 0

Remove parenthesis around (-14x + 9x2 + 3x3)
6x + -7x2 + 8x3 + -14x + 9x2 + 3x3 = 0

Reorder the terms:
6x + -14x + -7x2 + 9x2 + 8x3 + 3x3 = 0

Combine like terms: 6x + -14x = -8x
-8x + -7x2 + 9x2 + 8x3 + 3x3 = 0

Combine like terms: -7x2 + 9x2 = 2x2
-8x + 2x2 + 8x3 + 3x3 = 0

Combine like terms: 8x3 + 3x3 = 11x3
-8x + 2x2 + 11x3 = 0

Solving
-8x + 2x2 + 11x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-8 + 2x + 11x2) = 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 + 2x + 11x2)' equal to zero and attempt to solve:

Simplifying
-8 + 2x + 11x2 = 0

Solving
-8 + 2x + 11x2 = 0

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

Divide each side by '11'.
-0.7272727273 + 0.1818181818x + x2 = 0

Move the constant term to the right:

Add '0.7272727273' to each side of the equation.
-0.7272727273 + 0.1818181818x + 0.7272727273 + x2 = 0 + 0.7272727273

Reorder the terms:
-0.7272727273 + 0.7272727273 + 0.1818181818x + x2 = 0 + 0.7272727273

Combine like terms: -0.7272727273 + 0.7272727273 = 0.0000000000
0.0000000000 + 0.1818181818x + x2 = 0 + 0.7272727273
0.1818181818x + x2 = 0 + 0.7272727273

Combine like terms: 0 + 0.7272727273 = 0.7272727273
0.1818181818x + x2 = 0.7272727273

The x term is 0.1818181818x.  Take half its coefficient (0.0909090909).
Square it (0.008264462808) and add it to both sides.

Add '0.008264462808' to each side of the equation.
0.1818181818x + 0.008264462808 + x2 = 0.7272727273 + 0.008264462808

Reorder the terms:
0.008264462808 + 0.1818181818x + x2 = 0.7272727273 + 0.008264462808

Combine like terms: 0.7272727273 + 0.008264462808 = 0.735537190108
0.008264462808 + 0.1818181818x + x2 = 0.735537190108

Factor a perfect square on the left side:
(x + 0.0909090909)(x + 0.0909090909) = 0.735537190108

Calculate the square root of the right side: 0.857634648

Break this problem into two subproblems by setting 
(x + 0.0909090909) equal to 0.857634648 and -0.857634648.

Subproblem 1
x + 0.0909090909 = 0.857634648

Simplifying
x + 0.0909090909 = 0.857634648

Reorder the terms:
0.0909090909 + x = 0.857634648

Solving
0.0909090909 + x = 0.857634648

Solving for variable 'x'.

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

Add '-0.0909090909' to each side of the equation.
0.0909090909 + -0.0909090909 + x = 0.857634648 + -0.0909090909

Combine like terms: 0.0909090909 + -0.0909090909 = 0.0000000000
0.0000000000 + x = 0.857634648 + -0.0909090909
x = 0.857634648 + -0.0909090909

Combine like terms: 0.857634648 + -0.0909090909 = 0.7667255571
x = 0.7667255571

Simplifying
x = 0.7667255571

Subproblem 2
x + 0.0909090909 = -0.857634648

Simplifying
x + 0.0909090909 = -0.857634648

Reorder the terms:
0.0909090909 + x = -0.857634648

Solving
0.0909090909 + x = -0.857634648

Solving for variable 'x'.

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

Add '-0.0909090909' to each side of the equation.
0.0909090909 + -0.0909090909 + x = -0.857634648 + -0.0909090909

Combine like terms: 0.0909090909 + -0.0909090909 = 0.0000000000
0.0000000000 + x = -0.857634648 + -0.0909090909
x = -0.857634648 + -0.0909090909

Combine like terms: -0.857634648 + -0.0909090909 = -0.9485437389
x = -0.9485437389

Simplifying
x = -0.9485437389

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.7667255571, -0.9485437389}
Solution
x = {0, 0.7667255571, -0.9485437389}