Find the products for the following:
`(3x+2)(x-3)`

Answer

To find the product of the expression \((3x + 2)(x - 3)\), we will use the distributive property (also known as the FOIL method for binomials). Here’s a step-by-step solution:

### Step 1: Distribute \(3x\) to both terms in the second bracket \((x - 3)\)
Multiply \(3x\) by \(x\) and then by \(-3\):
\[ 3x \cdot x = 3x^2 \]
\[ 3x \cdot (-3) = -9x \]

### Step 2: Distribute \(2\) to both terms in the second bracket \((x - 3)\)
Multiply \(2\) by \(x\) and then by \(-3\):
\[ 2 \cdot x = 2x \]
\[ 2 \cdot (-3) = -6 \]

### Step 3: Combine all the results from the distributions
Now, we add all the results from Step 1 and Step 2:
\[ 3x^2 - 9x + 2x - 6 \]

### Step 4: Combine like terms
Combine the \(x\) terms:
\[ -9x + 2x = -7x \]
So, the expression simplifies to:
\[ 3x^2 - 7x - 6 \]

### Final Answer
Thus, the product of the expression \((3x + 2)(x - 3)\) is:
\[ \boxed{3x^2 - 7x - 6} \]

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