To solve the equation [tex]\(12x^2 - 36x = 0\)[/tex], we can follow these steps:
1. Factor the equation:
Notice that we can factor out a common term from each part of the equation:
[tex]\[
12x^2 - 36x = 12x(x - 3)
\][/tex]
This shows that the equation can be rewritten as:
[tex]\[
12x(x - 3) = 0
\][/tex]
2. Set each factor equal to zero:
For the product of two factors to be zero, at least one of the factors must be zero. Hence, we set each factor to zero and solve for [tex]\(x\)[/tex]:
[tex]\[
12x = 0 \quad \text{or} \quad x - 3 = 0
\][/tex]
3. Solve each equation:
- Solving [tex]\(12x = 0\)[/tex]:
[tex]\[
x = 0
\][/tex]
- Solving [tex]\(x - 3 = 0\)[/tex]:
[tex]\[
x = 3
\][/tex]
4. Identify the solutions:
The solutions to the equation [tex]\(12x^2 - 36x = 0\)[/tex] are:
[tex]\[
x = 0 \quad \text{and} \quad x = 3
\][/tex]
5. Select the correct answer:
Comparing the solutions [tex]\(x = 0\)[/tex] and [tex]\(x = 3\)[/tex] with the provided options:
- A. [tex]\(x = 0, 3\)[/tex]
- B. [tex]\(x = 0, \frac{1}{3}\)[/tex]
- C. [tex]\(x = 0, -3\)[/tex]
- D. [tex]\(x = \frac{1}{4}, 3\)[/tex]
The correct answer is:
[tex]\[
\boxed{A. \, x = 0, 3}
\][/tex]
