8x^3-27x=0

Solution for 8x^3-27x=0 equation:

Simplifying
8x3 + -27x = 0

Reorder the terms:
-27x + 8x3 = 0

Solving
-27x + 8x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-27 + 8x2) = 0

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 '(-27 + 8x2)' equal to zero and attempt to solve:

Simplifying
-27 + 8x2 = 0

Solving
-27 + 8x2 = 0

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

Add '27' to each side of the equation.
-27 + 27 + 8x2 = 0 + 27

Combine like terms: -27 + 27 = 0
0 + 8x2 = 0 + 27
8x2 = 0 + 27

Combine like terms: 0 + 27 = 27
8x2 = 27

Divide each side by '8'.
x2 = 3.375

Simplifying
x2 = 3.375

Take the square root of each side:
x = {-1.837117307, 1.837117307}
Solution
x = {0, -1.837117307, 1.837117307}