Problem of the Week

Updated at Sep 7, 2026 10:54 AM

To get more practice in equation, we brought you this problem of the week:

How can we solve the equation \(\frac{4(m-3)}{2+\frac{5}{m}}=\frac{8}{3}\)?

Check out the solution below!



\[\frac{4(m-3)}{2+\frac{5}{m}}=\frac{8}{3}\]

1
Multiply both sides by \(2+\frac{5}{m}\).
\[4(m-3)=\frac{8}{3}(2+\frac{5}{m})\]

2
Multiply both sides by \(3\).
\[12(m-3)=8(2+\frac{5}{m})\]

3
Expand.
\[12m-36=16+\frac{40}{m}\]

4
Multiply both sides by \(m\).
\[12{m}^{2}-36m=16m+40\]

5
Move all terms to one side.
\[12{m}^{2}-36m-16m-40=0\]

6
Simplify  \(12{m}^{2}-36m-16m-40\)  to  \(12{m}^{2}-52m-40\).
\[12{m}^{2}-52m-40=0\]

7
Factor out the common term \(4\).
\[4(3{m}^{2}-13m-10)=0\]

8
Split the second term in \(3{m}^{2}-13m-10\) into two terms.
\[4(3{m}^{2}+2m-15m-10)=0\]

9
Factor out common terms in the first two terms, then in the last two terms.
\[4(m(3m+2)-5(3m+2))=0\]

10
Factor out the common term \(3m+2\).
\[4(3m+2)(m-5)=0\]

11
Solve for \(m\).
\[m=-\frac{2}{3},5\]

Done

Decimal Form: -0.666667, 5
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