## Solving the Equation (x+4)(x-3) = -10

This article will guide you through the steps of solving the equation (x+4)(x-3) = -10. We'll use algebraic techniques to find the solutions for *x*.

### Expanding the Equation

The first step is to expand the left side of the equation by multiplying the binomials:

(x+4)(x-3) = x² + x - 12

Now, the equation becomes:

x² + x - 12 = -10

### Rearranging the Equation

To solve the quadratic equation, we need to set it equal to zero. Add 10 to both sides of the equation:

x² + x - 2 = 0

### Factoring the Quadratic Equation

The equation is now in standard quadratic form. We can solve it by factoring:

(x+2)(x-1) = 0

For the product of two factors to be zero, at least one of the factors must be zero. Therefore, we have two possible solutions:

**x + 2 = 0****x - 1 = 0**

Solving for *x* in each case:

**x = -2****x = 1**

### Verifying the Solutions

To ensure our solutions are correct, we can substitute them back into the original equation:

- For
**x = -2**: (-2 + 4)(-2 - 3) = (2)(-5) = -10 - For
**x = 1**: (1 + 4)(1 - 3) = (5)(-2) = -10

Both solutions satisfy the original equation, confirming our answers.

### Conclusion

The solutions for the equation (x+4)(x-3) = -10 are **x = -2** and **x = 1**. By expanding, rearranging, and factoring the equation, we were able to find the values of *x* that make the equation true.