Solve the following equations :
`(x-5)(x+3)=(x-7)(x+4)`

Answer

To solve the equation \((x-5)(x+3)=(x-7)(x+4)\), we will follow these steps:

### Step 1: Expand both sides of the equation
We will start by expanding the left side and the right side of the equation.

**Left Side:**
\[ (x-5)(x+3) = x^2 + 3x - 5x - 15 = x^2 - 2x - 15 \]

**Right Side:**
\[ (x-7)(x+4) = x^2 + 4x - 7x - 28 = x^2 - 3x - 28 \]

So, the equation becomes:
\[ x^2 - 2x - 15 = x^2 - 3x - 28 \]

### Step 2: Simplify the equation
Next, we will simplify the equation by eliminating \(x^2\) from both sides.

Subtract \(x^2\) from both sides:
\[ -2x - 15 = -3x - 28 \]

### Step 3: Move all terms involving \(x\) to one side
Now, we will move all terms involving \(x\) to one side and the constant terms to the other side.

Add \(3x\) to both sides:
\[ -2x + 3x - 15 = -28 \]
This simplifies to:
\[ x - 15 = -28 \]

### Step 4: Move the constant term to the other side
Now, we will add \(15\) to both sides to isolate \(x\):
\[ x = -28 + 15 \]
This simplifies to:
\[ x = -13 \]

### Final Answer
The solution to the equation is:
\[ \boxed{-13} \]

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