Task 3:

	Solve the equation x⋅(x^2+3x)=0.

To solve the equation \( x \cdot (x^2 + 3x) = 0 \), let's follow these steps:

### Step 1: Apply the Zero-Product Property
The equation is already factored, so we can use the zero-product property, which states that if the product of two expressions is zero, then at least one of the expressions must be zero.

### Step 2: Set Each Factor Equal to Zero
We have two factors in the equation:
1. \( x = 0 \)
2. \( x^2 + 3x = 0 \)

### Step 3: Solve Each Equation

1. For the first factor:
   \[
   x = 0
   \]
   This is one solution.

2. For the second factor:
   \[
   x^2 + 3x = 0
   \]
   We can factor this as:
   \[
   x(x + 3) = 0
   \]
   Again, using the zero-product property, we set each factor to zero:
   - \( x = 0 \) (This solution is the same as the one we already found.)
   - \( x + 3 = 0 \) which simplifies to \( x = -3 \).

### Step 4: Combine the Solutions
The solutions to the equation \( x \cdot (x^2 + 3x) = 0 \) are:
\[
x = 0 \quad \text{and} \quad x = -3
\]

### Final Answer
The solutions are \( x = 0 \) and \( x = -3 \).

Would you like more details or have any questions about this solution?

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Here are 5 related questions to further explore the topic:

1. How would you solve the equation \( x(x^2 - 4x) = 0 \)?
2. What are the roots of the quadratic equation \( x^2 + 3x = 0 \) without factoring?
3. How can you determine the number of solutions to a quadratic equation?
4. What happens when you have a cubic equation with one factor equal to zero?
5. How would you solve the equation \( x^2 + 5x + 6 = 0 \)?

**Tip:** Always look for common factors when solving polynomial equations, as they simplify the solving process significantly.

Learn how to solve the equation x⋅(x^2+3x)=0 with a detailed step-by-step solution. This problem involves applying the zero-product property in algebra, suitable for Grades 7-9 students.

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