Problem of the Week

Updated at Dec 21, 2020 2:08 PM

This week we have another equation problem:

How would you solve \(t(4t-3)=27\)?

Let's start!



\[t(4t-3)=27\]

1
Expand.
\[4{t}^{2}-3t=27\]

2
Move all terms to one side.
\[4{t}^{2}-3t-27=0\]

3
Split the second term in \(4{t}^{2}-3t-27\) into two terms.
\[4{t}^{2}+9t-12t-27=0\]

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

5
Factor out the common term \(4t+9\).
\[(4t+9)(t-3)=0\]

6
Solve for \(t\).
\[t=-\frac{9}{4},3\]

Done

Decimal Form: -2.25, 3
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