If `a=4, b=-3, c=2`, find the value of `4a^(2)+5b-12c`..

Answer

To solve the expression \(4a^2 + 5b - 12c\) given the values \(a = 4\), \(b = -3\), and \(c = 2\), we will substitute the values into the expression step by step.

### Step 1: Substitute the values into the expression
We start with the expression:
\[ 4a^2 + 5b - 12c \]
Substituting the values \(a = 4\), \(b = -3\), and \(c = 2\):
\[ 4(4^2) + 5(-3) - 12(2) \]

### Step 2: Calculate \(a^2\)
Next, we calculate \(4^2\):
\[ 4^2 = 16 \]
Now substitute this back into the expression:
\[ 4(16) + 5(-3) - 12(2) \]

### Step 3: Multiply \(4\) by \(16\)
Now, we calculate \(4 \times 16\):
\[ 4 \times 16 = 64 \]
So the expression becomes:
\[ 64 + 5(-3) - 12(2) \]

### Step 4: Calculate \(5(-3)\)
Next, we calculate \(5 \times -3\):
\[ 5 \times -3 = -15 \]
Now substitute this back into the expression:
\[ 64 - 15 - 12(2) \]

### Step 5: Calculate \(12(2)\)
Now, we calculate \(12 \times 2\):
\[ 12 \times 2 = 24 \]
So the expression now looks like:
\[ 64 - 15 - 24 \]

### Step 6: Combine the terms
Now we combine the terms:
First, calculate \(64 - 15\):
\[ 64 - 15 = 49 \]
Now subtract \(24\):
\[ 49 - 24 = 25 \]

### Final Answer
Thus, the value of the expression \(4a^2 + 5b - 12c\) is:
\[ \boxed{25} \]