(9x)-(6x^3)=0

Solution for (9x)-(6x^3)=0 equation:

Simplifying
(9x) + -1(6x3) = 0

Remove parenthesis around (6x3)
(9x) + -1 * 6x3 = 0

Multiply -1 * 6
(9x) + -6x3 = 0

Solving
(9x) + -6x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(3 + -2x2) = 0

Ignore the factor 3.
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 + -2x2)' equal to zero and attempt to solve:

Simplifying
3 + -2x2 = 0

Solving
3 + -2x2 = 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 + -2x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x2 = 0 + -3
-2x2 = 0 + -3

Combine like terms: 0 + -3 = -3
-2x2 = -3

Divide each side by '-2'.
x2 = 1.5

Simplifying
x2 = 1.5

Take the square root of each side:
x = {-1.224744871, 1.224744871}
Solution
x = {0, -1.224744871, 1.224744871}