Question: Solve the following equation by factoring.
x² - 16x = 0
Part 1 of 2
Rewrite the equation in a completely factored form.
x(x - 16) = 0
Part 2 of 2
The solution set is { }.
(Simplify your answer. Use a comma to separate answers as needed.)
1. **State the problem:** Solve the equation $$x^2 - 16x = 0$$ by factoring.
2. **Factor the equation:**
We look for common factors in both terms. Both terms have a factor of $$x$$.
So, $$x^2 - 16x = x(x - 16)$$.
3. **Set each factor equal to zero:**
By the zero product property, if $$x(x - 16) = 0$$, then either
$$x = 0$$ or $$x - 16 = 0$$.
4. **Solve each equation:**
- For $$x = 0$$, the solution is $$x = 0$$.
- For $$x - 16 = 0$$, add $$16$$ to both sides:
$$x = 16$$.
5. **Write the solution set:**
The solutions are $$x = 0$$ and $$x = 16$$.
So, the solution set is $$\{0, 16\}$$.