# 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