Solving the Equation (x + 4)(x  1) = 0
This equation is a simple quadratic equation in factored form. To find the solutions, we can use the Zero Product Property.
The Zero Product Property
The Zero Product Property states that if the product of two or more factors is equal to zero, then at least one of the factors must be equal to zero.
Solving the Equation

Identify the factors: In the equation (x + 4)(x  1) = 0, the factors are (x + 4) and (x  1).

Set each factor equal to zero:
 x + 4 = 0
 x  1 = 0

Solve for x:
 x = 4
 x = 1
The Solutions
Therefore, the solutions to the equation (x + 4)(x  1) = 0 are x = 4 and x = 1.
Verification
We can verify our solutions by substituting them back into the original equation:
 For x = 4: (4 + 4)(4  1) = 0 * 5 = 0. This is true.
 For x = 1: (1 + 4)(1  1) = 5 * 0 = 0. This is also true.
Therefore, our solutions are correct.