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Solve by factoring.

27 x squared minus 9 x equals 0
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Part 1
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1 answer

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