Solve the following equations :
`(3x+2)/(x-6)=-7`

Answer

To solve the equation \((3x + 2)/(x - 6) = -7\), we will follow these steps:

### Step 1: Cross Multiply
We start with the equation:
\[ \frac{3x + 2}{x - 6} = -7 \]
Cross multiplying gives us:
\[ 3x + 2 = -7(x - 6) \]

### Step 2: Distribute the Right Side
Now we will distribute \(-7\) on the right side:
\[ 3x + 2 = -7x + 42 \]

### Step 3: Move Variable Terms to One Side
Next, we want to get all the variable terms on one side and the constant terms on the other. We can do this by adding \(7x\) to both sides:
\[ 3x + 7x + 2 = 42 \]
This simplifies to:
\[ 10x + 2 = 42 \]

### Step 4: Move Constant Terms to the Other Side
Now, we will subtract \(2\) from both sides:
\[ 10x = 42 - 2 \]
This simplifies to:
\[ 10x = 40 \]

### Step 5: Solve for \(x\)
Finally, we divide both sides by \(10\):
\[ x = \frac{40}{10} \]
This gives us:
\[ x = 4 \]

### Final Answer
Thus, the solution to the equation is:
\[ \boxed{4} \]