X2/3-x=2x/3-x

To solve the equation \( \frac{x^2}{3} - x = \frac{2x}{3} - x \), we can follow these steps:

1. First, simplify both sides of the equation.
2. Combine like terms.

Starting with the original equation:

\[ \frac{x^2}{3} - x = \frac{2x}{3} - x \]

Subtract \(-x\) from both sides:

\[ \frac{x^2}{3} - x + x = \frac{2x}{3} - x + x \]

This simplifies to:

\[ \frac{x^2}{3} = \frac{2x}{3} \]

Now, multiply both sides by 3 to eliminate the fractions:

\[ x^2 = 2x \]

Next, move all terms to one side to set the equation to zero:

\[ x^2 - 2x = 0 \]

Now, factor the left side:

\[ x(x - 2) = 0 \]

Setting each factor to zero gives us the solutions:

1. \( x = 0 \)
2. \( x - 2 = 0 \) which gives \( x = 2 \)

Thus, the solutions to the equation \( \frac{x^2}{3} - x = \frac{2x}{3} - x \) are:

\[ \boxed{0 \text{ and } 2} \]