Question

3x² + 12x = 0

Explanation:

Step1: Factor out the GCF

The greatest common factor (GCF) of \(3x^2\) and \(12x\) is \(3x\). Factoring it out, we get:
\(3x(x + 4)=0\)

Step2: Apply the zero - product property

The zero - product property states that if \(ab = 0\), then either \(a = 0\) or \(b = 0\) (or both). So we set each factor equal to zero:

• For \(3x=0\), dividing both sides by 3 gives \(x = 0\).
• For \(x + 4=0\), subtracting 4 from both sides gives \(x=-4\).

Answer:

The solutions are \(x = 0\) and \(x=-4\)