To solve the equation \( 3x^2 = 2x \), we can start by rearranging it to set it to zero:
\[ 3x^2 - 2x = 0 \]
Next, we can factor out \( x \) from the left side:
\[ x(3x - 2) = 0 \]
Now, we can set each factor equal to zero:
- \( x = 0 \)
- \( 3x - 2 = 0 \)
For the second equation, we solve for \( x \):
\[ 3x - 2 = 0 \ 3x = 2 \ x = \frac{2}{3} \]
So the solutions to the equation \( 3x^2 = 2x \) are:
\[ x = 0 \quad \text{and} \quad x = \frac{2}{3} \]