Problem of the Week

Updated at Jan 19, 2026 12:10 PM

This week's problem comes from the equation category.

How would you solve the equation \(16{t}^{2}(t+2)=48\)?

Let's begin!



\[16{t}^{2}(t+2)=48\]

1
Expand.
\[16{t}^{3}+32{t}^{2}=48\]

2
Move all terms to one side.
\[16{t}^{3}+32{t}^{2}-48=0\]

3
Factor out the common term \(16\).
\[16({t}^{3}+2{t}^{2}-3)=0\]

4
Factor \({t}^{3}+2{t}^{2}-3\) using Polynomial Division.
\[16({t}^{2}+3t+3)(t-1)=0\]

5
Solve for \(t\).
\[t=1\]

6
Use the Quadratic Formula.
\[t=\frac{-3+\sqrt{3}\imath }{2},\frac{-3-\sqrt{3}\imath }{2}\]

7
Collect all solutions from the previous steps.
\[t=1,\frac{-3+\sqrt{3}\imath }{2},\frac{-3-\sqrt{3}\imath }{2}\]

Done
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