(6X^5-9X^3-9X)+(2X^5+2X^3+2X)=0

Solution for (6X^5-9X^3-9X)+(2X^5+2X^3+2X)=0 equation:

Simplifying
(6X5 + -9X3 + -9X) + (2X5 + 2X3 + 2X) = 0

Reorder the terms:
(-9X + -9X3 + 6X5) + (2X5 + 2X3 + 2X) = 0

Remove parenthesis around (-9X + -9X3 + 6X5)
-9X + -9X3 + 6X5 + (2X5 + 2X3 + 2X) = 0

Reorder the terms:
-9X + -9X3 + 6X5 + (2X + 2X3 + 2X5) = 0

Remove parenthesis around (2X + 2X3 + 2X5)
-9X + -9X3 + 6X5 + 2X + 2X3 + 2X5 = 0

Reorder the terms:
-9X + 2X + -9X3 + 2X3 + 6X5 + 2X5 = 0

Combine like terms: -9X + 2X = -7X
-7X + -9X3 + 2X3 + 6X5 + 2X5 = 0

Combine like terms: -9X3 + 2X3 = -7X3
-7X + -7X3 + 6X5 + 2X5 = 0

Combine like terms: 6X5 + 2X5 = 8X5
-7X + -7X3 + 8X5 = 0

Solving
-7X + -7X3 + 8X5 = 0

Solving for variable 'X'.

Factor out the Greatest Common Factor (GCF), 'X'.
X(-7 + -7X2 + 8X4) = 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 + -7X2 + 8X4)' equal to zero and attempt to solve:

Simplifying
-7 + -7X2 + 8X4 = 0

Solving
-7 + -7X2 + 8X4 = 0

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

Divide each side by '8'.
-0.875 + -0.875X2 + X4 = 0

Move the constant term to the right:

Add '0.875' to each side of the equation.
-0.875 + -0.875X2 + 0.875 + X4 = 0 + 0.875

Reorder the terms:
-0.875 + 0.875 + -0.875X2 + X4 = 0 + 0.875

Combine like terms: -0.875 + 0.875 = 0.000
0.000 + -0.875X2 + X4 = 0 + 0.875
-0.875X2 + X4 = 0 + 0.875

Combine like terms: 0 + 0.875 = 0.875
-0.875X2 + X4 = 0.875

The X term is -0.875X2.  Take half its coefficient (-0.4375).
Square it (0.19140625) and add it to both sides.

Add '0.19140625' to each side of the equation.
-0.875X2 + 0.19140625 + X4 = 0.875 + 0.19140625

Reorder the terms:
0.19140625 + -0.875X2 + X4 = 0.875 + 0.19140625

Combine like terms: 0.875 + 0.19140625 = 1.06640625
0.19140625 + -0.875X2 + X4 = 1.06640625

Factor a perfect square on the left side:
(X2 + -0.4375)(X2 + -0.4375) = 1.06640625

Calculate the square root of the right side: 1.032669478

Break this problem into two subproblems by setting 
(X2 + -0.4375) equal to 1.032669478 and -1.032669478.

Subproblem 1
X2 + -0.4375 = 1.032669478

Simplifying
X2 + -0.4375 = 1.032669478

Reorder the terms:
-0.4375 + X2 = 1.032669478

Solving
-0.4375 + X2 = 1.032669478

Solving for variable 'X'.

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

Add '0.4375' to each side of the equation.
-0.4375 + 0.4375 + X2 = 1.032669478 + 0.4375

Combine like terms: -0.4375 + 0.4375 = 0.0000
0.0000 + X2 = 1.032669478 + 0.4375
X2 = 1.032669478 + 0.4375

Combine like terms: 1.032669478 + 0.4375 = 1.470169478
X2 = 1.470169478

Simplifying
X2 = 1.470169478

Take the square root of each side:
X = {-1.212505455, 1.212505455}

Subproblem 2
X2 + -0.4375 = -1.032669478

Simplifying
X2 + -0.4375 = -1.032669478

Reorder the terms:
-0.4375 + X2 = -1.032669478

Solving
-0.4375 + X2 = -1.032669478

Solving for variable 'X'.

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

Add '0.4375' to each side of the equation.
-0.4375 + 0.4375 + X2 = -1.032669478 + 0.4375

Combine like terms: -0.4375 + 0.4375 = 0.0000
0.0000 + X2 = -1.032669478 + 0.4375
X2 = -1.032669478 + 0.4375

Combine like terms: -1.032669478 + 0.4375 = -0.595169478
X2 = -0.595169478

Simplifying
X2 = -0.595169478

Reorder the terms:
0.595169478 + X2 = -0.595169478 + 0.595169478

Combine like terms: -0.595169478 + 0.595169478 = 0.000000000
0.595169478 + X2 = 0.000000000

The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
X = {0}