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To solve for all values of \( x \) where \( g(x) = 0 \), we start by analyzing the function \( g(x) \), which is given as:

\[
g(x) = (2x + 3)(x + 2)(x - 1)
\]

The function \( g(x) \) equals zero when any of the factors in the product equals zero. Therefore, we need to solve the following equations:

1. \( 2x + 3 = 0 \)
2. \( x + 2 = 0 \)
3. \( x - 1 = 0 \)

### Solving each equation:

1. \( 2x + 3 = 0 \)

\[
2x = -3
\]
\[
x = -\frac{3}{2}
\]

2. \( x + 2 = 0 \)

\[
x = -2
\]

3. \( x - 1 = 0 \)

\[
x = 1
\]

### Solution:

The values of \( x \) that satisfy \( g(x) = 0 \) are:

\[
x = -\frac{3}{2}, -2, 1
\]

Would you like more details or have any questions? Here are some related questions:

1. What are the roots of the function \( h(x) = 0 \) for the given \( h(x) \)?
2. How do the graphs of \( g(x) \) and \( h(x) \) compare?
3. Can \( g(x) \) have any maximum or minimum points? How would you find them?
4. What is the multiplicity of each root of \( g(x) \)?
5. How does factoring help in solving polynomial equations?

**Tip:** When solving polynomial equations, always check the factors individually to determine the roots of the equation.

Learn how to find the roots of the polynomial function g(x) = (2x + 3)(x + 2)(x - 1) using the zero product property. This problem is suitable for students in Grades 9-12 and covers key algebraic concepts including polynomial equations and factoring.

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