Question

solve $(2a - 6)(3a + 15) = 0$.

$a = \square, a = \square$

Explanation:

Step1: Apply zero - product property

If \((2a - 6)(3a+15)=0\), then either \(2a - 6 = 0\) or \(3a + 15=0\) (by the zero - product property: if \(ab = 0\), then \(a = 0\) or \(b = 0\)).

Step2: Solve \(2a-6 = 0\)

Add 6 to both sides of the equation \(2a-6 = 0\):
\(2a-6 + 6=0 + 6\)
\(2a=6\)
Divide both sides by 2:
\(\frac{2a}{2}=\frac{6}{2}\)
\(a = 3\)

Step3: Solve \(3a + 15=0\)

Subtract 15 from both sides of the equation \(3a + 15=0\):
\(3a+15-15=0 - 15\)
\(3a=-15\)
Divide both sides by 3:
\(\frac{3a}{3}=\frac{-15}{3}\)
\(a=- 5\)

Answer:

\(a = 3\), \(a=-5\)