# Problem of the Week

## Updated at Aug 22, 2022 11:23 AM

This week we have another equation problem:

How would you solve $$\frac{(t+2)(4t-3)}{5}=4$$?

Let's start!

$\frac{(t+2)(4t-3)}{5}=4$

 1 Multiply both sides by $$5$$.$(t+2)(4t-3)=20$2 Expand.$4{t}^{2}-3t+8t-6=20$3 Simplify  $$4{t}^{2}-3t+8t-6$$  to  $$4{t}^{2}+5t-6$$.$4{t}^{2}+5t-6=20$4 Move all terms to one side.$4{t}^{2}+5t-6-20=0$5 Simplify  $$4{t}^{2}+5t-6-20$$  to  $$4{t}^{2}+5t-26$$.$4{t}^{2}+5t-26=0$6 Split the second term in $$4{t}^{2}+5t-26$$ into two terms.1 Multiply the coefficient of the first term by the constant term.$4\times -26=-104$2 Ask: Which two numbers add up to $$5$$ and multiply to $$-104$$?$$13$$ and $$-8$$3 Split $$5t$$ as the sum of $$13t$$ and $$-8t$$.$4{t}^{2}+13t-8t-26$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$4{t}^{2}+13t-8t-26=0$7 Factor out common terms in the first two terms, then in the last two terms.$t(4t+13)-2(4t+13)=0$8 Factor out the common term $$4t+13$$.$(4t+13)(t-2)=0$9 Solve for $$t$$.1 Ask: When will $$(4t+13)(t-2)$$ equal zero?When $$4t+13=0$$ or $$t-2=0$$2 Solve each of the 2 equations above.$t=-\frac{13}{4},2$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$t=-\frac{13}{4},2$DoneDecimal Form: -3.25, 2t=-13/4,2