x^3-6x-72x=0

Solution for x^3-6x-72x=0 equation:

Simplifying
x3 + -6x + -72x = 0

Reorder the terms:
-6x + -72x + x3 = 0

Combine like terms: -6x + -72x = -78x
-78x + x3 = 0

Solving
-78x + x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-78 + x2) = 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 '(-78 + x2)' equal to zero and attempt to solve:

Simplifying
-78 + x2 = 0

Solving
-78 + x2 = 0

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

Add '78' to each side of the equation.
-78 + 78 + x2 = 0 + 78

Combine like terms: -78 + 78 = 0
0 + x2 = 0 + 78
x2 = 0 + 78

Combine like terms: 0 + 78 = 78
x2 = 78

Simplifying
x2 = 78

Take the square root of each side:
x = {-8.831760866, 8.831760866}
Solution
x = {0, -8.831760866, 8.831760866}