(7x^3-4x^2+8x)+(8x^3+6x^2-14x)=

Solution for (7x^3-4x^2+8x)+(8x^3+6x^2-14x)= equation:

Simplifying
(7x3 + -4x2 + 8x) + (8x3 + 6x2 + -14x) = 0

Reorder the terms:
(8x + -4x2 + 7x3) + (8x3 + 6x2 + -14x) = 0

Remove parenthesis around (8x + -4x2 + 7x3)
8x + -4x2 + 7x3 + (8x3 + 6x2 + -14x) = 0

Reorder the terms:
8x + -4x2 + 7x3 + (-14x + 6x2 + 8x3) = 0

Remove parenthesis around (-14x + 6x2 + 8x3)
8x + -4x2 + 7x3 + -14x + 6x2 + 8x3 = 0

Reorder the terms:
8x + -14x + -4x2 + 6x2 + 7x3 + 8x3 = 0

Combine like terms: 8x + -14x = -6x
-6x + -4x2 + 6x2 + 7x3 + 8x3 = 0

Combine like terms: -4x2 + 6x2 = 2x2
-6x + 2x2 + 7x3 + 8x3 = 0

Combine like terms: 7x3 + 8x3 = 15x3
-6x + 2x2 + 15x3 = 0

Solving
-6x + 2x2 + 15x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-6 + 2x + 15x2) = 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 '(-6 + 2x + 15x2)' equal to zero and attempt to solve:

Simplifying
-6 + 2x + 15x2 = 0

Solving
-6 + 2x + 15x2 = 0

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

Divide each side by '15'.
-0.4 + 0.1333333333x + x2 = 0

Move the constant term to the right:

Add '0.4' to each side of the equation.
-0.4 + 0.1333333333x + 0.4 + x2 = 0 + 0.4

Reorder the terms:
-0.4 + 0.4 + 0.1333333333x + x2 = 0 + 0.4

Combine like terms: -0.4 + 0.4 = 0.0
0.0 + 0.1333333333x + x2 = 0 + 0.4
0.1333333333x + x2 = 0 + 0.4

Combine like terms: 0 + 0.4 = 0.4
0.1333333333x + x2 = 0.4

The x term is 0.1333333333x.  Take half its coefficient (0.06666666665).
Square it (0.004444444442) and add it to both sides.

Add '0.004444444442' to each side of the equation.
0.1333333333x + 0.004444444442 + x2 = 0.4 + 0.004444444442

Reorder the terms:
0.004444444442 + 0.1333333333x + x2 = 0.4 + 0.004444444442

Combine like terms: 0.4 + 0.004444444442 = 0.404444444442
0.004444444442 + 0.1333333333x + x2 = 0.404444444442

Factor a perfect square on the left side:
(x + 0.06666666665)(x + 0.06666666665) = 0.404444444442

Calculate the square root of the right side: 0.635959468

Break this problem into two subproblems by setting 
(x + 0.06666666665) equal to 0.635959468 and -0.635959468.

Subproblem 1
x + 0.06666666665 = 0.635959468

Simplifying
x + 0.06666666665 = 0.635959468

Reorder the terms:
0.06666666665 + x = 0.635959468

Solving
0.06666666665 + x = 0.635959468

Solving for variable 'x'.

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

Add '-0.06666666665' to each side of the equation.
0.06666666665 + -0.06666666665 + x = 0.635959468 + -0.06666666665

Combine like terms: 0.06666666665 + -0.06666666665 = 0.00000000000
0.00000000000 + x = 0.635959468 + -0.06666666665
x = 0.635959468 + -0.06666666665

Combine like terms: 0.635959468 + -0.06666666665 = 0.56929280135
x = 0.56929280135

Simplifying
x = 0.56929280135

Subproblem 2
x + 0.06666666665 = -0.635959468

Simplifying
x + 0.06666666665 = -0.635959468

Reorder the terms:
0.06666666665 + x = -0.635959468

Solving
0.06666666665 + x = -0.635959468

Solving for variable 'x'.

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

Add '-0.06666666665' to each side of the equation.
0.06666666665 + -0.06666666665 + x = -0.635959468 + -0.06666666665

Combine like terms: 0.06666666665 + -0.06666666665 = 0.00000000000
0.00000000000 + x = -0.635959468 + -0.06666666665
x = -0.635959468 + -0.06666666665

Combine like terms: -0.635959468 + -0.06666666665 = -0.70262613465
x = -0.70262613465

Simplifying
x = -0.70262613465

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.56929280135, -0.70262613465}
Solution
x = {0, 0.56929280135, -0.70262613465}