a^3-48a=0

Solution for a^3-48a=0 equation:

Simplifying
a3 + -48a = 0

Reorder the terms:
-48a + a3 = 0

Solving
-48a + a3 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'a'.
a(-48 + a2) = 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 '(-48 + a2)' equal to zero and attempt to solve:

Simplifying
-48 + a2 = 0

Solving
-48 + a2 = 0

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

Add '48' to each side of the equation.
-48 + 48 + a2 = 0 + 48

Combine like terms: -48 + 48 = 0
0 + a2 = 0 + 48
a2 = 0 + 48

Combine like terms: 0 + 48 = 48
a2 = 48

Simplifying
a2 = 48

Take the square root of each side:
a = {-6.92820323, 6.92820323}
Solution
a = {0, -6.92820323, 6.92820323}