2a*6x^3=x

To solve the equation \( 2a \cdot 6x^3 = x \), we can first simplify the left side:

\[ 12a x^3 = x \]

Next, we can rearrange the equation by getting all terms to one side:

\[ 12a x^3 - x = 0 \]

Factoring out \( x \):

\[ x(12a x^2 - 1) = 0 \]

This gives us two cases to consider:

1. \( x = 0 \)
2. \( 12a x^2 - 1 = 0 \)

For the second case, we can solve for \( x \):

\[ 12a x^2 = 1 \] \[ x^2 = \frac{1}{12a} \] \[ x = \pm \sqrt{\frac{1}{12a}} \]

Thus, the solutions to the equation \( 2a \cdot 6x^3 = x \) are:

\[ x = 0, \quad x = \sqrt{\frac{1}{12a}}, \quad x = -\sqrt{\frac{1}{12a}} \]

These are the values of \( x \) that satisfy the original equation.