Problem of the Week

Updated at Aug 22, 2022 11:23 AM

This week we have another equation problem:

How would you solve \(\frac{(t+2)(4t-3)}{5}=4\)?

Let's start!



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

1
Multiply both sides by \(5\).
\[(t+2)(4t-3)=20\]

2
Expand.
\[4{t}^{2}-3t+8t-6=20\]

3
Simplify  \(4{t}^{2}-3t+8t-6\)  to  \(4{t}^{2}+5t-6\).
\[4{t}^{2}+5t-6=20\]

4
Move all terms to one side.
\[4{t}^{2}+5t-6-20=0\]

5
Simplify  \(4{t}^{2}+5t-6-20\)  to  \(4{t}^{2}+5t-26\).
\[4{t}^{2}+5t-26=0\]

6
Split the second term in \(4{t}^{2}+5t-26\) into two terms.
\[4{t}^{2}+13t-8t-26=0\]

7
Factor out common terms in the first two terms, then in the last two terms.
\[t(4t+13)-2(4t+13)=0\]

8
Factor out the common term \(4t+13\).
\[(4t+13)(t-2)=0\]

9
Solve for \(t\).
\[t=-\frac{13}{4},2\]

Done

Decimal Form: -3.25, 2
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