24x^3-18x+6x=0

Solution for 24x^3-18x+6x=0 equation:

Simplifying
24x3 + -18x + 6x = 0

Reorder the terms:
-18x + 6x + 24x3 = 0

Combine like terms: -18x + 6x = -12x
-12x + 24x3 = 0

Solving
-12x + 24x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '12x'.
12x(-1 + 2x2) = 0

Ignore the factor 12.
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 '(-1 + 2x2)' equal to zero and attempt to solve:

Simplifying
-1 + 2x2 = 0

Solving
-1 + 2x2 = 0

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

Add '1' to each side of the equation.
-1 + 1 + 2x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 2x2 = 0 + 1
2x2 = 0 + 1

Combine like terms: 0 + 1 = 1
2x2 = 1

Divide each side by '2'.
x2 = 0.5

Simplifying
x2 = 0.5

Take the square root of each side:
x = {-0.707106781, 0.707106781}
Solution
x = {0, -0.707106781, 0.707106781}