# Problem of the Week

## Updated at Feb 26, 2024 9:23 AM

This week we have another equation problem:

How would you solve $$\frac{4(t-3)(2+t)}{3}=\frac{56}{3}$$?

Let's start!

$\frac{4(t-3)(2+t)}{3}=\frac{56}{3}$

 1 Multiply both sides by $$3$$.$4(t-3)(2+t)=56$2 Expand.$8t+4{t}^{2}-24-12t=56$3 Simplify  $$8t+4{t}^{2}-24-12t$$  to  $$-4t+4{t}^{2}-24$$.$-4t+4{t}^{2}-24=56$4 Move all terms to one side.$4t-4{t}^{2}+24+56=0$5 Simplify  $$4t-4{t}^{2}+24+56$$  to  $$4t-4{t}^{2}+80$$.$4t-4{t}^{2}+80=0$6 Factor out the common term $$4$$.$4(t-{t}^{2}+20)=0$7 Factor out the negative sign.$4\times -({t}^{2}-t-20)=0$8 Divide both sides by $$4$$.$-{t}^{2}+t+20=0$9 Multiply both sides by $$-1$$.${t}^{2}-t-20=0$10 Factor $${t}^{2}-t-20$$.1 Ask: Which two numbers add up to $$-1$$ and multiply to $$-20$$?$$-5$$ and $$4$$2 Rewrite the expression using the above.$(t-5)(t+4)$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$(t-5)(t+4)=0$11 Solve for $$t$$.1 Ask: When will $$(t-5)(t+4)$$ equal zero?When $$t-5=0$$ or $$t+4=0$$2 Solve each of the 2 equations above.$t=5,-4$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$t=5,-4$Donet=5,-4