Simplify the following
`4x-(3x+3)-[2x-4[x+3(x-5)}]`

Answer

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

### Step 1: Distribute the negative sign
Start by distributing the negative sign in front of the parentheses and brackets.
\[ 4x - (3x + 3) = 4x - 3x - 3 \]
So, the expression becomes:
\[ 4x - 3x - 3 - [2x - 4[x + 3(x - 5)]] \]

### Step 2: Simplify the expression inside the brackets
Now, we need to simplify the expression inside the square brackets:
\[ 4[x + 3(x - 5)] \]
First, simplify \(3(x - 5)\):
\[ 3(x - 5) = 3x - 15 \]
Now substitute this back:
\[ x + 3(x - 5) = x + 3x - 15 = 4x - 15 \]
Now multiply by 4:
\[ 4(4x - 15) = 16x - 60 \]
So, the expression inside the brackets now becomes:
\[ 2x - (16x - 60) \]

### Step 3: Distribute the negative sign again
Now distribute the negative sign:
\[ 2x - 16x + 60 \]
This simplifies to:
\[ -14x + 60 \]

### Step 4: Substitute back into the main expression
Now substitute this back into the main expression:
\[ 4x - 3x - 3 - (-14x + 60) \]
This simplifies to:
\[ 4x - 3x - 3 + 14x - 60 \]

### Step 5: Combine like terms
Now combine all the \(x\) terms and the constant terms:
\[ (4x - 3x + 14x) + (-3 - 60) = 15x - 63 \]

### Final Answer
Thus, the simplified expression is:
\[ \boxed{15x - 63} \]