To solve the equation \( 142n = 41 \) using the factorization method, we'll first express the equation in a more standard form. We can rewrite it as:
\[ 142n - 41 = 0 \]
Now we can rearrange the equation to isolate \( n \):
\[ 142n = 41 \]
Next, divide both sides by 142 to solve for \( n \):
\[ n = \frac{41}{142} \]
Now, we can simplify this fraction. Notice that \( 41 \) and \( 142 \) share a common factor of \( 41 \):
\[ n = \frac{41 \div 41}{142 \div 41} = \frac{1}{3.48} \approx 0.287 \]
Thus, the solution is:
\[ n = \frac{1}{3.48} \]
This is the solution for \( n \) using algebraic manipulation; however, the term "factorization method" typically applies to polynomial equations rather than simple linear equations like this one. If you meant something else or have a different context in mind, please let me know!