8x^3-48x=0

Solution for 8x^3-48x=0 equation:

Simplifying
8x3 + -48x = 0

Reorder the terms:
-48x + 8x3 = 0

Solving
-48x + 8x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '8x'.
8x(-6 + x2) = 0

Ignore the factor 8.
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 + x2)' equal to zero and attempt to solve:

Simplifying
-6 + x2 = 0

Solving
-6 + x2 = 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 + x2 = 0 + 6

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

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

Simplifying
x2 = 6

Take the square root of each side:
x = {-2.449489743, 2.449489743}
Solution
x = {0, -2.449489743, 2.449489743}