To solve the given equation [tex]\(-s^2 + 8s = 0\)[/tex], let's proceed with the following steps:
1. Rewrite the equation: Start with the given equation:
[tex]\[
-s^2 + 8s = 0
\][/tex]
2. Factor the equation: Factor out the common term. In this case, [tex]\(s\)[/tex] is common to both terms:
[tex]\[
-s(s - 8) = 0
\][/tex]
3. Set each factor to zero: For the product to be zero, at least one of the factors must be zero. Therefore, set each factor equal to zero:
[tex]\[
-s = 0 \quad \text{or} \quad s - 8 = 0
\][/tex]
4. Solve for [tex]\(s\)[/tex]:
- For [tex]\(-s = 0\)[/tex]:
[tex]\[
s = 0
\][/tex]
- For [tex]\(s - 8 = 0\)[/tex]:
[tex]\[
s = 8
\][/tex]
Thus, the solution set for the equation [tex]\(-s^2 + 8s = 0\)[/tex] is:
[tex]\[
0, 8
\][/tex]
