To solve the quadratic equation \(46x^2 - 138x = 0\) by factoring out the greatest common factor (GCF), we first identify the GCF of the terms in the equation.

Question

The GCF of \(46x^2\) and \(-138x\) is \(46x\).

Now, we can factor out \(46x\) from the equation:

\[
46x(x - 3 = 0)
\]

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

1. Setting the first factor equal to zero:
\[
46x = 0
\]
Dividing both sides by 46:
\[
x = 0
\]

2. Setting the second factor equal to zero:
\[
x - 3 = 0
\]
Adding 3 to both sides:
\[
x = 3
\]

Thus, the solutions to the quadratic equation \(46x^2 - 138x = 0\) are:
\[
x = 0 \quad \text{and} \quad x = 3
\]
make this like a 6th gradr wrote it

Answer 1

To solve the equation \(46x^2 - 138x = 0\), we first need to find the greatest common factor (GCF) of the two terms.

1. Identify the GCF: The GCF of \(46x^2\) and \(-138x\) is \(46x\).

2. Factor out the GCF: We can take \(46x\) out of the equation: \[ 46x(x - 3) = 0 \]

3. Set each factor to zero: Now, we will set each part of the equation equal to zero and solve for \(x\).

   • First, we set the first factor, \(46x\), equal to zero: \[ 46x = 0 \] To solve for \(x\), we divide both sides by 46: \[ x = 0 \]

   • Now, we set the second factor, \(x - 3\), equal to zero: \[ x - 3 = 0 \] To solve for \(x\), we add 3 to both sides: \[ x = 3 \]

4. The solutions: So, the answers to the equation \(46x^2 - 138x = 0\) are: \[ x = 0 \quad \text{and} \quad x = 3 \]

And that’s how you solve this quadratic equation by factoring!