(x+4)(x-3)=-10

2 min read Jun 16, 2024

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.