(x*x*x)-12(x*x)+27x=0

Solution for (x*x*x)-12(x*x)+27x=0 equation:

Simplifying
(x * x * x) + -12(x * x) + 27x = 0

Multiply x * x
(x2 * x) + -12(x * x) + 27x = 0

Multiply x2 * x
(x3) + -12(x * x) + 27x = 0
x3 + -12(x * x) + 27x = 0

Multiply x * x
x3 + -12(x2) + 27x = 0

Reorder the terms:
27x + -12x2 + x3 = 0

Solving
27x + -12x2 + x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(27 + -12x + x2) = 0

Factor a trinomial.
x((3 + -1x)(9 + -1x)) = 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 '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Subproblem 3
Set the factor '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {0, 3, 9}