3a^5-3a^3-36a=0

Solution for 3a^5-3a^3-36a=0 equation:

Simplifying
3a5 + -3a3 + -36a = 0

Reorder the terms:
-36a + -3a3 + 3a5 = 0

Solving
-36a + -3a3 + 3a5 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3a'.
3a(-12 + -1a2 + a4) = 0

Factor a trinomial.
3a((-3 + -1a2)(4 + -1a2)) = 0

Factor a difference between two squares.
3a((-3 + -1a2)((2 + a)(2 + -1a))) = 0

Ignore the factor 3.
Subproblem 1
Set the factor 'a' equal to zero and attempt to solve:

Simplifying
a = 0

Solving
a = 0

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

Simplifying
a = 0
Subproblem 2
Set the factor '(-3 + -1a2)' equal to zero and attempt to solve:

Simplifying
-3 + -1a2 = 0

Solving
-3 + -1a2 = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1a2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1a2 = 0 + 3
-1a2 = 0 + 3

Combine like terms: 0 + 3 = 3
-1a2 = 3

Divide each side by '-1'.
a2 = -3

Simplifying
a2 = -3

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 '(2 + a)' equal to zero and attempt to solve:

Simplifying
2 + a = 0

Solving
2 + a = 0

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

Add '-2' to each side of the equation.
2 + -2 + a = 0 + -2

Combine like terms: 2 + -2 = 0
0 + a = 0 + -2
a = 0 + -2

Combine like terms: 0 + -2 = -2
a = -2

Simplifying
a = -2
Subproblem 4
Set the factor '(2 + -1a)' equal to zero and attempt to solve:

Simplifying
2 + -1a = 0

Solving
2 + -1a = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1a = 0 + -2

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

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

Divide each side by '-1'.
a = 2

Simplifying
a = 2
Solution
a = {0, -2, 2}