Problem of the Week

Updated at May 2, 2022 3:27 PM

How can we solve the equation \(4{(3-y)}^{2}(y+2)=24\)?

Below is the solution.



\[4{(3-y)}^{2}(y+2)=24\]

1
Expand.
\[36y+72-24{y}^{2}-48y+4{y}^{3}+8{y}^{2}=24\]

2
Simplify  \(36y+72-24{y}^{2}-48y+4{y}^{3}+8{y}^{2}\)  to  \(-12y+72-16{y}^{2}+4{y}^{3}\).
\[-12y+72-16{y}^{2}+4{y}^{3}=24\]

3
Move all terms to one side.
\[12y-72+16{y}^{2}-4{y}^{3}+24=0\]

4
Simplify  \(12y-72+16{y}^{2}-4{y}^{3}+24\)  to  \(12y-48+16{y}^{2}-4{y}^{3}\).
\[12y-48+16{y}^{2}-4{y}^{3}=0\]

5
Factor out the common term \(4\).
\[4(3y-12+4{y}^{2}-{y}^{3})=0\]

6
Factor \(3y-12+4{y}^{2}-{y}^{3}\) using Polynomial Division.
\[4(-{y}^{2}+3)(y-4)=0\]

7
Solve for \(y\).
\[y=4,\pm \sqrt{3}\]

Done

Decimal Form: 4, ±1.732051
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