Question

1. solve for m:

-8m(m - 6) = 0
6
0
6, 0
m = 6
m = 6,0
enter your next step here

Explanation:

Step1: Apply Zero - Product Property

The Zero - Product Property states that if \(ab = 0\), then either \(a = 0\) or \(b=0\) (or both). For the equation \(-8m(m - 6)=0\), we can set each factor equal to zero.
We have two factors: \(-8m\) and \((m - 6)\).
First, consider the factor \(-8m\):
Set \(-8m=0\). Divide both sides of the equation by \(-8\):
\(m=\frac{0}{-8}=0\)

Step2: Consider the other factor

Now, consider the factor \((m - 6)\):
Set \(m - 6=0\). Add 6 to both sides of the equation:
\(m=6\)

Answer:

\(m = 0\) or \(m=6\) (or in the boxed form for the set of solutions \(\boxed{0,6}\))