Multiply
`2x - 5 " by " 3x+2`

Answer

To multiply the algebraic expressions \(2x - 5\) and \(3x + 2\), we can use the distributive property (also known as the FOIL method for binomials). Here’s a step-by-step solution:

### Step 1: Write down the expressions
We start with the expressions we want to multiply:
\[ (2x - 5)(3x + 2) \]

### Step 2: Distribute the first term of the first expression
We will first multiply \(2x\) by each term in the second expression \(3x + 2\):
\[ 2x \cdot 3x + 2x \cdot 2 \]
Calculating these:
\[ 2x \cdot 3x = 6x^2 \quad \text{and} \quad 2x \cdot 2 = 4x \]

### Step 3: Distribute the second term of the first expression
Next, we multiply \(-5\) by each term in the second expression \(3x + 2\):
\[ -5 \cdot 3x + (-5) \cdot 2 \]
Calculating these:
\[ -5 \cdot 3x = -15x \quad \text{and} \quad -5 \cdot 2 = -10 \]

### Step 4: Combine all the results
Now we combine all the terms we calculated:
\[ 6x^2 + 4x - 15x - 10 \]

### Step 5: Combine like terms
Now, we combine the like terms \(4x\) and \(-15x\):
\[ 6x^2 + (4x - 15x) - 10 = 6x^2 - 11x - 10 \]

### Final Answer
The final result of multiplying \(2x - 5\) by \(3x + 2\) is:
\[ \boxed{6x^2 - 11x - 10} \]

---