Solve by factoring.

Question

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: $$x=0,\frac{1}{3}$$