6x^5-51x^3-27x=0

Solution for 6x^5-51x^3-27x=0 equation:

Simplifying
6x5 + -51x3 + -27x = 0

Reorder the terms:
-27x + -51x3 + 6x5 = 0

Solving
-27x + -51x3 + 6x5 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(-9 + -17x2 + 2x4) = 0

Factor a trinomial.
3x((-1 + -2x2)(9 + -1x2)) = 0

Factor a difference between two squares.
3x((-1 + -2x2)((3 + x)(3 + -1x))) = 0

Ignore the factor 3.
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 '(-1 + -2x2)' equal to zero and attempt to solve:

Simplifying
-1 + -2x2 = 0

Solving
-1 + -2x2 = 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 + -2x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2x2 = 0 + 1
-2x2 = 0 + 1

Combine like terms: 0 + 1 = 1
-2x2 = 1

Divide each side by '-2'.
x2 = -0.5

Simplifying
x2 = -0.5

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 '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3
Subproblem 4
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {0, -3, 3}