Let's solve the quadratic equation step-by-step:

Given equation:

\[
5x^2 - 3x = 0
\]

1. **Factor out the common term**: Notice that each term contains an \(x\), so we can factor \(x\) out of the equation:

\[
x(5x - 3) = 0
\]

2. **Set each factor equal to zero**: According to the zero-product property, if the product of two factors is zero, then at least one of the factors must be zero. Therefore, we set each factor equal to zero:

\[
x = 0 \quad \text{or} \quad 5x - 3 = 0
\]

3. **Solve for \(x\) in each case**:

   - For the first equation, \(x = 0\).

   - For the second equation, solve for \(x\):

\[
5x - 3 = 0
\]

Add 3 to both sides:

\[
5x = 3
\]

Divide both sides by 5:

\[
x = \frac{3}{5}
\]

### Solutions:

The solutions to the equation are:

\[
x_1 = 0, \quad x_2 = \frac{3}{5}
\]

Would you like more details on any part of this solution?

Here are 5 questions to expand your understanding:

1. What is the zero-product property, and why is it useful for solving quadratic equations?
2. How do you factor out a common term from an expression?
3. What are some other methods for solving quadratic equations besides factoring?
4. How can you check if your solutions to a quadratic equation are correct?
5. What types of problems in real life can be modeled by quadratic equations?

**Tip:** When solving quadratic equations, always look for common factors first, as this can simplify the solving process significantly.

Learn how to solve the quadratic equation 5x^2 - 3x = 0 with a detailed step-by-step solution. This problem covers key algebraic concepts, including the quadratic equation formula, factoring, and the zero-product property theorem. Suitable for students in Grades 9-12.

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