6x^3=128x

Solution for 6x^3=128x equation:

Simplifying
6x3 = 128x

Solving
6x3 = 128x

Solving for variable 'x'.

Reorder the terms:
-128x + 6x3 = 128x + -128x

Combine like terms: 128x + -128x = 0
-128x + 6x3 = 0

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-64 + 3x2) = 0

Ignore the factor 2.
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 '(-64 + 3x2)' equal to zero and attempt to solve:

Simplifying
-64 + 3x2 = 0

Solving
-64 + 3x2 = 0

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

Add '64' to each side of the equation.
-64 + 64 + 3x2 = 0 + 64

Combine like terms: -64 + 64 = 0
0 + 3x2 = 0 + 64
3x2 = 0 + 64

Combine like terms: 0 + 64 = 64
3x2 = 64

Divide each side by '3'.
x2 = 21.33333333

Simplifying
x2 = 21.33333333

Take the square root of each side:
x = {-4.618802153, 4.618802153}
Solution
x = {0, -4.618802153, 4.618802153}