The expression $3x^3 - 4x^6$ is not an equation because it does not include an equals sign. To solve for $y$ in terms of $x$, we first set the expression equal to $y$:

$y = 3x^3 - 4x^6$

Derivative of $y$ with respect to $x$ (if needed):

If you're looking for the rate of change, the derivative of $y$ with respect to $x$ is:

$\frac{dy}{dx} = 9x^2 - 24x^5$

Finding Critical Points (if applicable):

To find where the function increases or decreases, set the derivative to zero:

$9x^2 - 24x^5 = 0$ $x^2(9 - 24x^3) = 0$

Thus: $x^2 = 0 \quad \text{or} \quad 9 - 24x^3 = 0$

For $x^2 = 0$: $x = 0$

For $9 - 24x^3 = 0$: $x^3 = \frac{9}{24} = \frac{3}{8}$ $x = \sqrt[3]{\frac{3}{8}}$

These points are useful if graphing or analyzing the behavior of $y$.

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Would you like to graph the function, analyze it further, or solve for $x$ in terms of a different condition? Let me know!