(7x^3-5x^2+8x)+(4x^3+7x^2-10x)=

Solution for (7x^3-5x^2+8x)+(4x^3+7x^2-10x)= equation:

Simplifying
(7x3 + -5x2 + 8x) + (4x3 + 7x2 + -10x) = 0

Reorder the terms:
(8x + -5x2 + 7x3) + (4x3 + 7x2 + -10x) = 0

Remove parenthesis around (8x + -5x2 + 7x3)
8x + -5x2 + 7x3 + (4x3 + 7x2 + -10x) = 0

Reorder the terms:
8x + -5x2 + 7x3 + (-10x + 7x2 + 4x3) = 0

Remove parenthesis around (-10x + 7x2 + 4x3)
8x + -5x2 + 7x3 + -10x + 7x2 + 4x3 = 0

Reorder the terms:
8x + -10x + -5x2 + 7x2 + 7x3 + 4x3 = 0

Combine like terms: 8x + -10x = -2x
-2x + -5x2 + 7x2 + 7x3 + 4x3 = 0

Combine like terms: -5x2 + 7x2 = 2x2
-2x + 2x2 + 7x3 + 4x3 = 0

Combine like terms: 7x3 + 4x3 = 11x3
-2x + 2x2 + 11x3 = 0

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

Solving for variable 'x'.

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

Simplifying
-2 + 2x + 11x2 = 0

Solving
-2 + 2x + 11x2 = 0

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

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

Move the constant term to the right:

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

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

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

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

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 = 0.1818181818 + 0.008264462808

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

Combine like terms: 0.1818181818 + 0.008264462808 = 0.190082644608
0.008264462808 + 0.1818181818x + x2 = 0.190082644608

Factor a perfect square on the left side:
(x + 0.0909090909)(x + 0.0909090909) = 0.190082644608

Calculate the square root of the right side: 0.435984684

Break this problem into two subproblems by setting 
(x + 0.0909090909) equal to 0.435984684 and -0.435984684.

Subproblem 1
x + 0.0909090909 = 0.435984684

Simplifying
x + 0.0909090909 = 0.435984684

Reorder the terms:
0.0909090909 + x = 0.435984684

Solving
0.0909090909 + x = 0.435984684

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 = 0.435984684 + -0.0909090909

Combine like terms: 0.0909090909 + -0.0909090909 = 0.0000000000
0.0000000000 + x = 0.435984684 + -0.0909090909
x = 0.435984684 + -0.0909090909

Combine like terms: 0.435984684 + -0.0909090909 = 0.3450755931
x = 0.3450755931

Simplifying
x = 0.3450755931

Subproblem 2
x + 0.0909090909 = -0.435984684

Simplifying
x + 0.0909090909 = -0.435984684

Reorder the terms:
0.0909090909 + x = -0.435984684

Solving
0.0909090909 + x = -0.435984684

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 = -0.435984684 + -0.0909090909

Combine like terms: 0.0909090909 + -0.0909090909 = 0.0000000000
0.0000000000 + x = -0.435984684 + -0.0909090909
x = -0.435984684 + -0.0909090909

Combine like terms: -0.435984684 + -0.0909090909 = -0.5268937749
x = -0.5268937749

Simplifying
x = -0.5268937749

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.3450755931, -0.5268937749}
Solution
x = {0, 0.3450755931, -0.5268937749}