## Solving the Equation (x+4)(x+6) = (x+1)(x+12)

This equation involves expanding brackets and simplifying to solve for the unknown variable 'x'. Let's break down the steps:

### 1. Expand the Brackets

**Left-hand side:**- (x+4)(x+6) = x(x+6) + 4(x+6) = x² + 6x + 4x + 24 = x² + 10x + 24

**Right-hand side:**- (x+1)(x+12) = x(x+12) + 1(x+12) = x² + 12x + x + 12 = x² + 13x + 12

### 2. Simplify the Equation

Now our equation becomes: x² + 10x + 24 = x² + 13x + 12

### 3. Solve for 'x'

**Subtract x² from both sides:**10x + 24 = 13x + 12**Subtract 10x from both sides:**24 = 3x + 12**Subtract 12 from both sides:**12 = 3x**Divide both sides by 3:**x = 4

### Solution

Therefore, the solution to the equation (x+4)(x+6) = (x+1)(x+12) is **x = 4**.

**Verification:**
We can substitute x = 4 back into the original equation to verify our answer:

- (4+4)(4+6) = (4+1)(4+12)
- (8)(10) = (5)(16)
- 80 = 80

This confirms that our solution x = 4 is correct.