## Solving the Quadratic Equation: (x+4)(x-3)+(x-5)(x+4)=0

This article will guide you through the steps to solve the quadratic equation: **(x+4)(x-3)+(x-5)(x+4)=0**.

### Step 1: Factor out the Common Term

Notice that both terms in the equation share the common factor **(x+4)**. We can factor it out:

**(x+4)(x-3) + (x-5)(x+4) = 0**

**(x+4)[(x-3) + (x-5)] = 0**

### Step 2: Simplify the Expression

Simplify the expression inside the brackets:

**(x+4)(2x - 8) = 0**

### Step 3: Apply the Zero Product Property

The Zero Product Property states that if the product of two factors is zero, then at least one of the factors must be zero. Therefore, we have two possible solutions:

**x + 4 = 0****2x - 8 = 0**

### Step 4: Solve for x

Solve each equation for x:

**x = -4****x = 4**

### Conclusion

Therefore, the solutions to the quadratic equation **(x+4)(x-3)+(x-5)(x+4)=0** are **x = -4** and **x = 4**.