Simplify : `3(4x^(2)-5x)+4(3x^(2)+5x)` and find the value for
`x= 3`

Answer

To simplify the expression \(3(4x^2 - 5x) + 4(3x^2 + 5x)\) and find the value for \(x = 3\), we will follow these steps:

### Step 1: Distribute the coefficients
We start by distributing the coefficients in front of the parentheses.

\[ 3(4x^2 - 5x) = 3 \cdot 4x^2 - 3 \cdot 5x = 12x^2 - 15x \]

\[ 4(3x^2 + 5x) = 4 \cdot 3x^2 + 4 \cdot 5x = 12x^2 + 20x \]

### Step 2: Combine the results
Now we combine the results from both distributions:

\[ 12x^2 - 15x + 12x^2 + 20x \]

### Step 3: Combine like terms
Next, we combine like terms:

- Combine \(12x^2 + 12x^2\):
\[ 12x^2 + 12x^2 = 24x^2 \]

- Combine \(-15x + 20x\):
\[ -15x + 20x = 5x \]

Putting it all together, we have:
\[ 24x^2 + 5x \]

### Step 4: Substitute \(x = 3\)
Now we substitute \(x = 3\) into the simplified expression:

\[ 24(3^2) + 5(3) \]

Calculating \(3^2\):
\[ 3^2 = 9 \]

Now substituting:
\[ 24(9) + 5(3) = 216 + 15 \]

### Step 5: Add the results
Finally, we add the two results together:
\[ 216 + 15 = 231 \]

### Final Answer
Thus, the value of the expression when \(x = 3\) is:
\[ \boxed{231} \]