Question

Solve by factoring.
27 x squared minus 9 x equals 0
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Part 1
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Answer 1

To solve the equation \( 27x^2 - 9x = 0 \) by factoring, we can first factor out the greatest common factor (GCF) from the terms on the left side of the equation.

1. Identify the GCF of \( 27x^2 \) and \( -9x \), which is \( 9x \).
2. Factor out \( 9x \):

\[
9x(3x - 1) = 0
\]

Now, we set each factor equal to zero and solve for \( x \):

1. \( 9x = 0 \)
- Dividing both sides by 9 gives \( x = 0 \).

2. \( 3x - 1 = 0 \)
- Adding 1 to both sides gives \( 3x = 1 \).
- Dividing both sides by 3 gives \( x = \frac{1}{3} \).

Thus, the solutions are:

\[
x = 0, \frac{1}{3}
\]

So, we can write the final answer as:

**Part 1:**
\[
x = 0, \frac{1}{3}
\]