Problem of the Week

Updated at Dec 21, 2020 2:08 PM

Recent Posts

Jan 25, 2021

This week we have another equation problem:

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

Let's start!

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

Expand.

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

Move all terms to one side.

\[4{t}^{2}-3t-27=0\]

Split the second term in \(4{t}^{2}-3t-27\) into two terms.

\[4{t}^{2}+9t-12t-27=0\]

Factor out common terms in the first two terms, then in the last two terms.

\[t(4t+9)-3(4t+9)=0\]

Factor out the common term \(4t+9\).

\[(4t+9)(t-3)=0\]

Solve for \(t\).

\[t=-\frac{9}{4},3\]

Done

Decimal Form: -2.25, 3