Problem of the Week

Updated at Aug 22, 2022 11:23 AM

This week we have another equation problem:

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

Let's start!



(t+2)(4t−3)5=4\frac{(t+2)(4t-3)}{5}=4

1
Multiply both sides by 55.
(t+2)(4t−3)=20(t+2)(4t-3)=20

2
Expand.
4t2−3t+8t−6=204{t}^{2}-3t+8t-6=20

3
Simplify  4t2−3t+8t−64{t}^{2}-3t+8t-6  to  4t2+5t−64{t}^{2}+5t-6.
4t2+5t−6=204{t}^{2}+5t-6=20

4
Move all terms to one side.
4t2+5t−6−20=04{t}^{2}+5t-6-20=0

5
Simplify  4t2+5t−6−204{t}^{2}+5t-6-20  to  4t2+5t−264{t}^{2}+5t-26.
4t2+5t−26=04{t}^{2}+5t-26=0

6
Split the second term in 4t2+5t−264{t}^{2}+5t-26 into two terms.
4t2+13t−8t−26=04{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)=0t(4t+13)-2(4t+13)=0

8
Factor out the common term 4t+134t+13.
(4t+13)(t−2)=0(4t+13)(t-2)=0

9
Solve for tt.
t=−134,2t=-\frac{13}{4},2

Done

Decimal Form: -3.25, 2
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