https://file.aiquickdraw.com/mathbot/file/17252178491845p96qnmm.jpg

The expression in the image is:

\[
x(2x - 3) = 0
\]

This is a quadratic equation that can be solved by setting each factor equal to zero:

1. **First factor**: \( x = 0 \)
   - This gives one solution: \( x = 0 \).

2. **Second factor**: \( 2x - 3 = 0 \)
   - Solve for \( x \) by adding 3 to both sides:
     \[
     2x = 3
     \]
   - Then, divide by 2:
     \[
     x = \frac{3}{2} = 1.5
     \]

So, the solutions to the equation are \( x = 0 \) and \( x = 1.5 \).

Would you like further details or have any questions?

Here are five related questions:
1. What is the significance of each factor in the equation?
2. How would the solution change if the equation was \( x(2x - 3) = 4 \)?
3. Can you graph the equation \( x(2x - 3) = 0 \) and identify the roots?
4. How would you solve \( x(2x - 3) = -6 \)?
5. What does the solution \( x = 0 \) represent in this context?

**Tip**: When you have a product of factors equal to zero, each factor can be set to zero to find all possible solutions.

Learn how to solve the quadratic equation x(2x - 3) = 0 step-by-step with detailed explanations and solutions for each factor. This problem covers the quadratic equation formula and the zero product property theorem. Suitable for students in Grades 7-9.

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