Question

solve ((x - 4)(3x + 10) = 0).
(x = 0) and (x = -\frac{10}{3})
(x = 0) or (x = 4)
(x = 4) or (x = -\frac{10}{3})
(x = 4) or (x = \frac{10}{3})

Explanation:

Step1: Apply Zero-Product Property

If \((x - 4)(3x + 10) = 0\), then either \(x - 4 = 0\) or \(3x + 10 = 0\) (by zero - product property: if \(ab = 0\), then \(a = 0\) or \(b = 0\)).

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

For the equation \(x - 4 = 0\), add 4 to both sides of the equation. We get \(x=4\).

Step3: Solve \(3x + 10 = 0\)

For the equation \(3x+10 = 0\), first subtract 10 from both sides: \(3x=- 10\). Then divide both sides by 3: \(x =-\frac{10}{3}\).

Answer:

\(x = 4\) or \(x=-\frac{10}{3}\) (corresponding to the option "x = 4 or x = -10/3")