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

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

Simplifying
(8x3 + -2x2 + 3x) + (5x3 + 5x2 + -10x) = 0

Reorder the terms:
(3x + -2x2 + 8x3) + (5x3 + 5x2 + -10x) = 0

Remove parenthesis around (3x + -2x2 + 8x3)
3x + -2x2 + 8x3 + (5x3 + 5x2 + -10x) = 0

Reorder the terms:
3x + -2x2 + 8x3 + (-10x + 5x2 + 5x3) = 0

Remove parenthesis around (-10x + 5x2 + 5x3)
3x + -2x2 + 8x3 + -10x + 5x2 + 5x3 = 0

Reorder the terms:
3x + -10x + -2x2 + 5x2 + 8x3 + 5x3 = 0

Combine like terms: 3x + -10x = -7x
-7x + -2x2 + 5x2 + 8x3 + 5x3 = 0

Combine like terms: -2x2 + 5x2 = 3x2
-7x + 3x2 + 8x3 + 5x3 = 0

Combine like terms: 8x3 + 5x3 = 13x3
-7x + 3x2 + 13x3 = 0

Solving
-7x + 3x2 + 13x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-7 + 3x + 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 + 3x + 13x2)' equal to zero and attempt to solve:

Simplifying
-7 + 3x + 13x2 = 0

Solving
-7 + 3x + 13x2 = 0

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

Divide each side by '13'.
-0.5384615385 + 0.2307692308x + x2 = 0

Move the constant term to the right:

Add '0.5384615385' to each side of the equation.
-0.5384615385 + 0.2307692308x + 0.5384615385 + x2 = 0 + 0.5384615385

Reorder the terms:
-0.5384615385 + 0.5384615385 + 0.2307692308x + x2 = 0 + 0.5384615385

Combine like terms: -0.5384615385 + 0.5384615385 = 0.0000000000
0.0000000000 + 0.2307692308x + x2 = 0 + 0.5384615385
0.2307692308x + x2 = 0 + 0.5384615385

Combine like terms: 0 + 0.5384615385 = 0.5384615385
0.2307692308x + x2 = 0.5384615385

The x term is 0.2307692308x.  Take half its coefficient (0.1153846154).
Square it (0.01331360947) and add it to both sides.

Add '0.01331360947' to each side of the equation.
0.2307692308x + 0.01331360947 + x2 = 0.5384615385 + 0.01331360947

Reorder the terms:
0.01331360947 + 0.2307692308x + x2 = 0.5384615385 + 0.01331360947

Combine like terms: 0.5384615385 + 0.01331360947 = 0.55177514797
0.01331360947 + 0.2307692308x + x2 = 0.55177514797

Factor a perfect square on the left side:
(x + 0.1153846154)(x + 0.1153846154) = 0.55177514797

Calculate the square root of the right side: 0.742815689

Break this problem into two subproblems by setting 
(x + 0.1153846154) equal to 0.742815689 and -0.742815689.

Subproblem 1
x + 0.1153846154 = 0.742815689

Simplifying
x + 0.1153846154 = 0.742815689

Reorder the terms:
0.1153846154 + x = 0.742815689

Solving
0.1153846154 + x = 0.742815689

Solving for variable 'x'.

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

Add '-0.1153846154' to each side of the equation.
0.1153846154 + -0.1153846154 + x = 0.742815689 + -0.1153846154

Combine like terms: 0.1153846154 + -0.1153846154 = 0.0000000000
0.0000000000 + x = 0.742815689 + -0.1153846154
x = 0.742815689 + -0.1153846154

Combine like terms: 0.742815689 + -0.1153846154 = 0.6274310736
x = 0.6274310736

Simplifying
x = 0.6274310736

Subproblem 2
x + 0.1153846154 = -0.742815689

Simplifying
x + 0.1153846154 = -0.742815689

Reorder the terms:
0.1153846154 + x = -0.742815689

Solving
0.1153846154 + x = -0.742815689

Solving for variable 'x'.

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

Add '-0.1153846154' to each side of the equation.
0.1153846154 + -0.1153846154 + x = -0.742815689 + -0.1153846154

Combine like terms: 0.1153846154 + -0.1153846154 = 0.0000000000
0.0000000000 + x = -0.742815689 + -0.1153846154
x = -0.742815689 + -0.1153846154

Combine like terms: -0.742815689 + -0.1153846154 = -0.8582003044
x = -0.8582003044

Simplifying
x = -0.8582003044

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.6274310736, -0.8582003044}
Solution
x = {0, 0.6274310736, -0.8582003044}