2x^5+10x^3-12x=0

Solution for 2x^5+10x^3-12x=0 equation:

Simplifying
2x5 + 10x3 + -12x = 0

Reorder the terms:
-12x + 10x3 + 2x5 = 0

Solving
-12x + 10x3 + 2x5 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-6 + 5x2 + x4) = 0

Factor a trinomial.
2x((-6 + -1x2)(1 + -1x2)) = 0

Factor a difference between two squares.
2x((-6 + -1x2)((1 + x)(1 + -1x))) = 0

Ignore the factor 2.
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 + -1x2)' equal to zero and attempt to solve:

Simplifying
-6 + -1x2 = 0

Solving
-6 + -1x2 = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1x2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x2 = 0 + 6
-1x2 = 0 + 6

Combine like terms: 0 + 6 = 6
-1x2 = 6

Divide each side by '-1'.
x2 = -6

Simplifying
x2 = -6

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 3
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 0

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

Add '-1' to each side of the equation.
1 + -1 + x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + x = 0 + -1
x = 0 + -1

Combine like terms: 0 + -1 = -1
x = -1

Simplifying
x = -1
Subproblem 4
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1x = 0 + -1
-1x = 0 + -1

Combine like terms: 0 + -1 = -1
-1x = -1

Divide each side by '-1'.
x = 1

Simplifying
x = 1
Solution
x = {0, -1, 1}