Problem of the Week

Updated at May 27, 2024 12:45 PM

This week's problem comes from the equation category.

How can we solve the equation \(\frac{(n-3)(n+2)}{25}=\frac{14}{25}\)?

Let's begin!



\[\frac{(n-3)(n+2)}{25}=\frac{14}{25}\]

1
Multiply both sides by \(25\).
\[(n-3)(n+2)=14\]

2
Expand.
\[{n}^{2}+2n-3n-6=14\]

3
Simplify  \({n}^{2}+2n-3n-6\)  to  \({n}^{2}-n-6\).
\[{n}^{2}-n-6=14\]

4
Move all terms to one side.
\[{n}^{2}-n-6-14=0\]

5
Simplify  \({n}^{2}-n-6-14\)  to  \({n}^{2}-n-20\).
\[{n}^{2}-n-20=0\]

6
Factor \({n}^{2}-n-20\).
\[(n-5)(n+4)=0\]

7
Solve for \(n\).
\[n=5,-4\]

Done
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