Question

solve for x .
(4x - 28)(x² + 10x + 21) = 0
(if there is more than one solution, separate them with commas.)
x =

Explanation:

Step1: Apply Zero-Product Property

If \(ab = 0\), then \(a = 0\) or \(b = 0\). So, set \(4x - 28 = 0\) and \(x^2 + 10x + 21 = 0\).

Step2: Solve \(4x - 28 = 0\)

Add 28 to both sides: \(4x = 28\).
Divide by 4: \(x = \frac{28}{4} = 7\).

Step3: Solve \(x^2 + 10x + 21 = 0\)

Factor the quadratic: \(x^2 + 10x + 21 = (x + 3)(x + 7) = 0\).
Set each factor to 0: \(x + 3 = 0\) or \(x + 7 = 0\).
Solve: \(x = -3\) or \(x = -7\).

Answer:

\(7, -3, -7\)