3x(2x− 9 4 ​ )=0 .

To solve the equation \(3x\left(2x - \frac{9}{4}\right) = 0\), we'll set each factor equal to zero and solve for \(x\).

1. First factor: \[ 3x = 0 \] Dividing both sides by 3 gives: \[ x = 0 \]

2. Second factor: \[ 2x - \frac{9}{4} = 0 \] Add \(\frac{9}{4}\) to both sides: \[ 2x = \frac{9}{4} \] Now, divide both sides by 2: \[ x = \frac{9}{4} \cdot \frac{1}{2} = \frac{9}{8} \]

Thus, the solutions to the equation \(3x\left(2x - \frac{9}{4}\right) = 0\) are: \[ x = 0 \quad \text{and} \quad x = \frac{9}{8} \]