Solve :
`13(x-4)-3(x-9)-5(x+4)=0`

Answer

To solve the equation \( 13(x-4) - 3(x-9) - 5(x+4) = 0 \), we will follow these steps:

### Step 1: Expand the brackets
We will distribute the numbers outside the brackets to the terms inside the brackets.

\[ 13(x-4) = 13x - 52 \]
\[ -3(x-9) = -3x + 27 \]
\[ -5(x+4) = -5x - 20 \]

Now, substituting these back into the equation gives:

\[ 13x - 52 - 3x + 27 - 5x - 20 = 0 \]

### Step 2: Combine like terms
Now, we will combine the \(x\) terms and the constant terms.

The \(x\) terms are:
\[ 13x - 3x - 5x = (13 - 3 - 5)x = 5x \]

The constant terms are:
\[ -52 + 27 - 20 = -52 + 27 - 20 = -45 \]

So, the equation simplifies to:
\[ 5x - 45 = 0 \]

### Step 3: Isolate \(x\)
Next, we will isolate \(x\) by adding 45 to both sides of the equation:

\[ 5x = 45 \]

### Step 4: Solve for \(x\)
Now, divide both sides by 5:

\[ x = \frac{45}{5} = 9 \]

### Final Answer
Thus, the solution to the equation is:
\[ \boxed{x = 9} \]

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