(x-2)(x+3)=6

2 min read Jun 17, 2024

Solving the Equation (x-2)(x+3) = 6

This equation presents a quadratic equation in a factored form. Let's break down the steps to solve it and find the values of x that satisfy the equation.

1. Expand the Equation

First, we need to expand the left side of the equation by multiplying the two binomials:

(x - 2)(x + 3) = x² + x - 6

Now, the equation becomes:

x² + x - 6 = 6

2. Rearrange into Standard Form

To solve a quadratic equation, we need to set it equal to zero. Subtract 6 from both sides:

x² + x - 12 = 0

3. Factor the Quadratic Expression

The quadratic expression on the left-hand side can be factored:

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

4. Solve for x

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

x + 4 = 0 which gives us x = -4
x - 3 = 0 which gives us x = 3

Conclusion

The solutions to the equation (x-2)(x+3) = 6 are x = -4 and x = 3.