Question

solve: (n - 7)(n + 4) = 0
options: {-7, 4}, {7, -4}, { -8/3, 8 }, {-5, 4}, { -3/8, -7 }

Explanation:

Step1: Apply Zero Product Property

If \((n - 7)(n + 4)=0\), then either \(n - 7 = 0\) or \(n + 4 = 0\) (by Zero Product Property: if \(ab = 0\), then \(a = 0\) or \(b = 0\)).

Step2: Solve for \(n\) in each equation

• For \(n - 7 = 0\), add 7 to both sides: \(n=7\).
• For \(n + 4 = 0\), subtract 4 from both sides: \(n=-4\).

Answer:

\(\{7, -4\}\) (corresponding to the option with set \(\{7, -4\}\))