Final answer:
To solve the equation (x - 5)(x + 1) = 7, factor or use the quadratic formula to find the solutions. The solutions are x = 6 or x = -2.
Step-by-step explanation:
To solve the equation (x - 5)(x + 1) = 7, you can start by multiplying the terms inside the parentheses using the distributive property.
This gives you x^2 - 4x - 5 = 7.
Next, bring all the terms to one side of the equation to form a quadratic equation: x^2 - 4x - 12 = 0. You can then factor or use the quadratic formula to find the solutions.
Factoring the quadratic equation x^2 - 4x - 12 = 0 gives you (x - 6)(x + 2) = 0. So, x = 6 or x = -2. These are the solutions to the original equation.