In each of the following find the value of 'a'
`4x^(2) + ax + 9 = (2x+ 3)^(2)`

Answer

To find the value of 'a' in the equation \( 4x^2 + ax + 9 = (2x + 3)^2 \), we can follow these steps:

### Step 1: Expand the right-hand side of the equation
We start with the equation:
\[ 4x^2 + ax + 9 = (2x + 3)^2 \]
Now, we will expand the right-hand side using the identity \( (a + b)^2 = a^2 + 2ab + b^2 \):
\[ (2x + 3)^2 = (2x)^2 + 2(2x)(3) + 3^2 \]
Calculating each term:
- \( (2x)^2 = 4x^2 \)
- \( 2(2x)(3) = 12x \)
- \( 3^2 = 9 \)

So, we have:
\[ (2x + 3)^2 = 4x^2 + 12x + 9 \]

### Step 2: Set the expanded form equal to the left-hand side
Now, we can rewrite our equation:
\[ 4x^2 + ax + 9 = 4x^2 + 12x + 9 \]

### Step 3: Compare coefficients
Next, we compare the coefficients of the terms on both sides of the equation. The coefficients of \( x^2 \) and the constant terms are already equal. Now we focus on the coefficients of \( x \):
\[ ax = 12x \]

### Step 4: Solve for 'a'
Since the coefficients of \( x \) must be equal, we can set:
\[ a = 12 \]

### Final Answer
Thus, the value of \( a \) is:
\[ \boxed{12} \]