Subtract: `2x^(2)-5x-3` from `4+x-3x^(2)`.

Answer

To solve the problem of subtracting \(2x^2 - 5x - 3\) from \(4 + x - 3x^2\), we will follow these steps:

### Step 1: Write the expression for subtraction
We need to subtract \(2x^2 - 5x - 3\) from \(4 + x - 3x^2\). This can be written as:
\[ (4 + x - 3x^2) - (2x^2 - 5x - 3) \]

### Step 2: Distribute the negative sign
When we subtract the second expression, we need to change the signs of each term in the expression \(2x^2 - 5x - 3\):
\[ 4 + x - 3x^2 - 2x^2 + 5x + 3 \]

### Step 3: Combine like terms
Now we will combine the like terms:
- Constant terms: \(4 + 3 = 7\)
- \(x\) terms: \(x + 5x = 6x\)
- \(x^2\) terms: \(-3x^2 - 2x^2 = -5x^2\)

Putting it all together, we have:
\[ 7 + 6x - 5x^2 \]

### Final Answer
Thus, the result of subtracting \(2x^2 - 5x - 3\) from \(4 + x - 3x^2\) is:
\[ -5x^2 + 6x + 7 \]

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