Let's translate the given statement into a mathematical equation and solve for the unknown number.

Statement: The product of three and the sum of a number and two is zero.

Translation to equation:
Let the unknown number be $x$.

The phrase "the product of three and the sum of a number and two" can be written as: $3(x + 2)$

According to the statement, this product equals zero: $3(x + 2) = 0$

Now, let's solve for $x$.

1. Divide both sides of the equation by 3: $x + 2 = 0$

2. Subtract 2 from both sides to isolate $x$: $x = -2$

Solution:
The unknown number is $x = -2$.

Would you like more details or have any questions?

Related Questions

1. What would the equation look like if the number is instead replaced by 5?
2. How would you solve an equation if it was given as $4(x + 3) = 0$?
3. Can you find the number if the product of five and the sum of the number and four is zero?
4. How does the solution change if the equation is $3(x - 2) = 0$?
5. How can you verify that your solution to $3(x + 2) = 0$ is correct?

Tip: Always check your solution by substituting the value back into the original equation to verify if it satisfies the equation.