a^3-36a=0

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

Simplifying
a3 + -36a = 0

Reorder the terms:
-36a + a3 = 0

Solving
-36a + a3 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'a'.
a(-36 + a2) = 0

Factor a difference between two squares.
a((6 + a)(-6 + a)) = 0

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

Simplifying
6 + a = 0

Solving
6 + a = 0

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

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

Combine like terms: 6 + -6 = 0
0 + a = 0 + -6
a = 0 + -6

Combine like terms: 0 + -6 = -6
a = -6

Simplifying
a = -6
Subproblem 3
Set the factor '(-6 + a)' equal to zero and attempt to solve:

Simplifying
-6 + a = 0

Solving
-6 + a = 0

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

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

Combine like terms: -6 + 6 = 0
0 + a = 0 + 6
a = 0 + 6

Combine like terms: 0 + 6 = 6
a = 6

Simplifying
a = 6
Solution
a = {0, -6, 6}