Simplify:`(3a+4)(2a-3)+(5a-4)(a+2)`.

Answer

To simplify the expression \((3a + 4)(2a - 3) + (5a - 4)(a + 2)\), we will follow these steps:

### Step 1: Expand the first product \((3a + 4)(2a - 3)\)

Using the distributive property (also known as the FOIL method for binomials):

\[ (3a + 4)(2a - 3) = 3a \cdot 2a + 3a \cdot (-3) + 4 \cdot 2a + 4 \cdot (-3) \]

Calculating each term:

- \(3a \cdot 2a = 6a^2\)
- \(3a \cdot (-3) = -9a\)
- \(4 \cdot 2a = 8a\)
- \(4 \cdot (-3) = -12\)

Combining these, we get:

\[ 6a^2 - 9a + 8a - 12 \]

### Step 2: Combine like terms from the first product

Now, we combine the like terms \(-9a\) and \(8a\):

\[ 6a^2 - 9a + 8a - 12 = 6a^2 - a - 12 \]

### Step 3: Expand the second product \((5a - 4)(a + 2)\)

Again using the distributive property:

\[ (5a - 4)(a + 2) = 5a \cdot a + 5a \cdot 2 + (-4) \cdot a + (-4) \cdot 2 \]

Calculating each term:

- \(5a \cdot a = 5a^2\)
- \(5a \cdot 2 = 10a\)
- \(-4 \cdot a = -4a\)
- \(-4 \cdot 2 = -8\)

Combining these, we get:

\[ 5a^2 + 10a - 4a - 8 \]

### Step 4: Combine like terms from the second product

Now, we combine the like terms \(10a\) and \(-4a\):

\[ 5a^2 + 10a - 4a - 8 = 5a^2 + 6a - 8 \]

### Step 5: Combine the results from both products

Now we will add the results from Step 2 and Step 4:

\[ (6a^2 - a - 12) + (5a^2 + 6a - 8) \]

Combining like terms:

- For \(a^2\): \(6a^2 + 5a^2 = 11a^2\)
- For \(a\): \(-a + 6a = 5a\)
- For the constant terms: \(-12 - 8 = -20\)

Thus, we get:

\[ 11a^2 + 5a - 20 \]

### Final Answer

The simplified expression is:

\[ \boxed{11a^2 + 5a - 20} \]