(-6x^3+60x^2-4x-2)+(x^3-x^2-4x+2)=

Solution for (-6x^3+60x^2-4x-2)+(x^3-x^2-4x+2)= equation:

Simplifying
(-6x3 + 60x2 + -4x + -2) + (x3 + -1x2 + -4x + 2) = 0

Reorder the terms:
(-2 + -4x + 60x2 + -6x3) + (x3 + -1x2 + -4x + 2) = 0

Remove parenthesis around (-2 + -4x + 60x2 + -6x3)
-2 + -4x + 60x2 + -6x3 + (x3 + -1x2 + -4x + 2) = 0

Reorder the terms:
-2 + -4x + 60x2 + -6x3 + (2 + -4x + -1x2 + x3) = 0

Remove parenthesis around (2 + -4x + -1x2 + x3)
-2 + -4x + 60x2 + -6x3 + 2 + -4x + -1x2 + x3 = 0

Reorder the terms:
-2 + 2 + -4x + -4x + 60x2 + -1x2 + -6x3 + x3 = 0

Combine like terms: -2 + 2 = 0
0 + -4x + -4x + 60x2 + -1x2 + -6x3 + x3 = 0
-4x + -4x + 60x2 + -1x2 + -6x3 + x3 = 0

Combine like terms: -4x + -4x = -8x
-8x + 60x2 + -1x2 + -6x3 + x3 = 0

Combine like terms: 60x2 + -1x2 = 59x2
-8x + 59x2 + -6x3 + x3 = 0

Combine like terms: -6x3 + x3 = -5x3
-8x + 59x2 + -5x3 = 0

Solving
-8x + 59x2 + -5x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-8 + 59x + -5x2) = 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 + 59x + -5x2)' equal to zero and attempt to solve:

Simplifying
-8 + 59x + -5x2 = 0

Solving
-8 + 59x + -5x2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
1.6 + -11.8x + x2 = 0

Move the constant term to the right:

Add '-1.6' to each side of the equation.
1.6 + -11.8x + -1.6 + x2 = 0 + -1.6

Reorder the terms:
1.6 + -1.6 + -11.8x + x2 = 0 + -1.6

Combine like terms: 1.6 + -1.6 = 0.0
0.0 + -11.8x + x2 = 0 + -1.6
-11.8x + x2 = 0 + -1.6

Combine like terms: 0 + -1.6 = -1.6
-11.8x + x2 = -1.6

The x term is -11.8x.  Take half its coefficient (-5.9).
Square it (34.81) and add it to both sides.

Add '34.81' to each side of the equation.
-11.8x + 34.81 + x2 = -1.6 + 34.81

Reorder the terms:
34.81 + -11.8x + x2 = -1.6 + 34.81

Combine like terms: -1.6 + 34.81 = 33.21
34.81 + -11.8x + x2 = 33.21

Factor a perfect square on the left side:
(x + -5.9)(x + -5.9) = 33.21

Calculate the square root of the right side: 5.762811814

Break this problem into two subproblems by setting 
(x + -5.9) equal to 5.762811814 and -5.762811814.

Subproblem 1
x + -5.9 = 5.762811814

Simplifying
x + -5.9 = 5.762811814

Reorder the terms:
-5.9 + x = 5.762811814

Solving
-5.9 + x = 5.762811814

Solving for variable 'x'.

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

Add '5.9' to each side of the equation.
-5.9 + 5.9 + x = 5.762811814 + 5.9

Combine like terms: -5.9 + 5.9 = 0.0
0.0 + x = 5.762811814 + 5.9
x = 5.762811814 + 5.9

Combine like terms: 5.762811814 + 5.9 = 11.662811814
x = 11.662811814

Simplifying
x = 11.662811814

Subproblem 2
x + -5.9 = -5.762811814

Simplifying
x + -5.9 = -5.762811814

Reorder the terms:
-5.9 + x = -5.762811814

Solving
-5.9 + x = -5.762811814

Solving for variable 'x'.

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

Add '5.9' to each side of the equation.
-5.9 + 5.9 + x = -5.762811814 + 5.9

Combine like terms: -5.9 + 5.9 = 0.0
0.0 + x = -5.762811814 + 5.9
x = -5.762811814 + 5.9

Combine like terms: -5.762811814 + 5.9 = 0.137188186
x = 0.137188186

Simplifying
x = 0.137188186

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.662811814, 0.137188186}
Solution
x = {0, 11.662811814, 0.137188186}