Question

46x^2 - 138x = 0
Solve by factoring out the GCF

Answer 1

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

1. The GCF of \( 46 \) and \( 138 \) is \( 46 \).
2. Both terms also have a factor of \( x \).

Thus, the GCF of the entire expression is \( 46x \).

Now, we can factor out the GCF from the equation:

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

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

1. \( 46x = 0 \)
- Dividing both sides by \( 46 \) gives:
\[
x = 0
\]

2. \( x - 3 = 0 \)
- Adding \( 3 \) to both sides gives:
\[
x = 3
\]

Thus, the solutions to the equation \( 46x^2 - 138x = 0 \) are:

\[
\boxed{0} \quad \text{and} \quad \boxed{3}
\]