Solve 3x2+27x=0

Question

3
𝑥
2
+
27
𝑥
=
0
by factoring out the greatest common factor.(2 points)
x =
𝑥

=


x=
𝑥
=

Answer 1

To solve the equation \(3x^2 + 27x = 0\) by factoring out the greatest common factor (GCF), we can follow these steps:

1. Identify the GCF in the terms \(3x^2\) and \(27x\). The GCF is \(3x\).

2. Factor out the GCF:

   \[ 3x(x + 9) = 0 \]

3. Set each factor equal to zero:

   \[ 3x = 0 \quad \text{or} \quad x + 9 = 0 \]

4. Solve for \(x\):

   • For \(3x = 0\):

     \[ x = 0 \]

   • For \(x + 9 = 0\):

     \[ x = -9 \]

So the solutions are:

\[ x = 0 \quad \text{or} \quad x = -9 \]

Final answer: \[ x = 0, \quad x = -9 \]