x^3=27x

Solution for x^3=27x equation:

Simplifying
x3 = 27x

Solving
x3 = 27x

Solving for variable 'x'.

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

Combine like terms: 27x + -27x = 0
-27x + x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-27 + 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 '(-27 + x2)' equal to zero and attempt to solve:

Simplifying
-27 + x2 = 0

Solving
-27 + x2 = 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 + x2 = 0 + 27

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

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

Simplifying
x2 = 27

Take the square root of each side:
x = {-5.196152423, 5.196152423}
Solution
x = {0, -5.196152423, 5.196152423}