(x+6)(x-1)=0

2 min read Jun 17, 2024

Solving the Equation (x+6)(x-1)=0

This equation is a quadratic equation in factored form. To solve for the values of x that satisfy this equation, we can use the Zero Product Property.

Zero Product Property

The Zero Product Property states that if the product of two or more factors is zero, then at least one of the factors must be zero.

In our equation, (x+6)(x-1) = 0, we have two factors: (x+6) and (x-1). For the product to be zero, either one or both of these factors must be equal to zero.

Solving for x

Let's set each factor equal to zero and solve for x:

x + 6 = 0 Subtract 6 from both sides: x = -6
x - 1 = 0 Add 1 to both sides: x = 1

Solutions

Therefore, the solutions to the equation (x+6)(x-1)=0 are x = -6 and x = 1. These values of x make the equation true.

Verification

We can verify our solutions by plugging them back into the original equation:

For x = -6: (-6 + 6)(-6 - 1) = 0 * -7 = 0. This is true.
For x = 1: (1 + 6)(1 - 1) = 7 * 0 = 0. This is also true.

This confirms that our solutions are correct.