(8x^3-2x^2+5x)+(6x^3+5x^2-12x)=

Solution for (8x^3-2x^2+5x)+(6x^3+5x^2-12x)= equation:

Simplifying
(8x3 + -2x2 + 5x) + (6x3 + 5x2 + -12x) = 0

Reorder the terms:
(5x + -2x2 + 8x3) + (6x3 + 5x2 + -12x) = 0

Remove parenthesis around (5x + -2x2 + 8x3)
5x + -2x2 + 8x3 + (6x3 + 5x2 + -12x) = 0

Reorder the terms:
5x + -2x2 + 8x3 + (-12x + 5x2 + 6x3) = 0

Remove parenthesis around (-12x + 5x2 + 6x3)
5x + -2x2 + 8x3 + -12x + 5x2 + 6x3 = 0

Reorder the terms:
5x + -12x + -2x2 + 5x2 + 8x3 + 6x3 = 0

Combine like terms: 5x + -12x = -7x
-7x + -2x2 + 5x2 + 8x3 + 6x3 = 0

Combine like terms: -2x2 + 5x2 = 3x2
-7x + 3x2 + 8x3 + 6x3 = 0

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

Solving
-7x + 3x2 + 14x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-7 + 3x + 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 '(-7 + 3x + 14x2)' equal to zero and attempt to solve:

Simplifying
-7 + 3x + 14x2 = 0

Solving
-7 + 3x + 14x2 = 0

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

Divide each side by '14'.
-0.5 + 0.2142857143x + x2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + 0.2142857143x + 0.5 + x2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + 0.2142857143x + x2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + 0.2142857143x + x2 = 0 + 0.5
0.2142857143x + x2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
0.2142857143x + x2 = 0.5

The x term is 0.2142857143x.  Take half its coefficient (0.1071428572).
Square it (0.01147959185) and add it to both sides.

Add '0.01147959185' to each side of the equation.
0.2142857143x + 0.01147959185 + x2 = 0.5 + 0.01147959185

Reorder the terms:
0.01147959185 + 0.2142857143x + x2 = 0.5 + 0.01147959185

Combine like terms: 0.5 + 0.01147959185 = 0.51147959185
0.01147959185 + 0.2142857143x + x2 = 0.51147959185

Factor a perfect square on the left side:
(x + 0.1071428572)(x + 0.1071428572) = 0.51147959185

Calculate the square root of the right side: 0.715178014

Break this problem into two subproblems by setting 
(x + 0.1071428572) equal to 0.715178014 and -0.715178014.

Subproblem 1
x + 0.1071428572 = 0.715178014

Simplifying
x + 0.1071428572 = 0.715178014

Reorder the terms:
0.1071428572 + x = 0.715178014

Solving
0.1071428572 + x = 0.715178014

Solving for variable 'x'.

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

Add '-0.1071428572' to each side of the equation.
0.1071428572 + -0.1071428572 + x = 0.715178014 + -0.1071428572

Combine like terms: 0.1071428572 + -0.1071428572 = 0.0000000000
0.0000000000 + x = 0.715178014 + -0.1071428572
x = 0.715178014 + -0.1071428572

Combine like terms: 0.715178014 + -0.1071428572 = 0.6080351568
x = 0.6080351568

Simplifying
x = 0.6080351568

Subproblem 2
x + 0.1071428572 = -0.715178014

Simplifying
x + 0.1071428572 = -0.715178014

Reorder the terms:
0.1071428572 + x = -0.715178014

Solving
0.1071428572 + x = -0.715178014

Solving for variable 'x'.

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

Add '-0.1071428572' to each side of the equation.
0.1071428572 + -0.1071428572 + x = -0.715178014 + -0.1071428572

Combine like terms: 0.1071428572 + -0.1071428572 = 0.0000000000
0.0000000000 + x = -0.715178014 + -0.1071428572
x = -0.715178014 + -0.1071428572

Combine like terms: -0.715178014 + -0.1071428572 = -0.8223208712
x = -0.8223208712

Simplifying
x = -0.8223208712

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.6080351568, -0.8223208712}
Solution
x = {0, 0.6080351568, -0.8223208712}