What is the solution set of (x – 5) (x + 1) = 16?1 pointA. {–3, 1}B. {–3, 7}C. {1, 7}D. {3, 9}

To solve the equation (x – 5) (x + 1) = 16, follow these steps:

Step 1: Expand the left side of the equation. This gives us x^2 - 5x + x - 5 = 16, which simplifies to x^2 - 4x - 5 = 16.

Step 2: Subtract 16 from both sides to set the equation to zero. This gives us x^2 - 4x - 21 = 0.

Step 3: Factor the quadratic equation. The factors of -21 that add up to -4 are -7 and 3. So, the factored form of the equation is (x - 7)(x + 3) = 0.

Step 4: Set each factor equal to zero and solve for x. This gives us x - 7 = 0 and x + 3 = 0. Solving these gives us x = 7 and x = -3.

So, the solution set of the equation (x – 5) (x + 1) = 16 is {–3, 7}, which corresponds to option B.