SOLUTION: 5t^-16t=-12 i have tried everything. please help me. I am so greatful for this site and your time. thank you so much. This is factoring equations.

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Question 149304: 5t^-16t=-12
i have tried everything. please help me. I am so greatful for this site and your time. thank you so much. This is factoring equations.
Found 2 solutions by jim_thompson5910, vleith:
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
Start with the given equation.


Add 12 to both sides.


Now let's factor the left side






Looking at the expression , we can see that the first coefficient is , the second coefficient is , and the last term is .


Now multiply the first coefficient by the last term to get .


Now the question is: what two whole numbers multiply to (the previous product) and add to the second coefficient ?


To find these two numbers, we need to list all of the factors of (the previous product).


Factors of :
1,2,3,4,5,6,10,12,15,20,30,60
-1,-2,-3,-4,-5,-6,-10,-12,-15,-20,-30,-60


Note: list the negative of each factor. This will allow us to find all possible combinations.


These factors pair up and multiply to .
1*60
2*30
3*20
4*15
5*12
6*10
(-1)*(-60)
(-2)*(-30)
(-3)*(-20)
(-4)*(-15)
(-5)*(-12)
(-6)*(-10)

Now let's add up each pair of factors to see if one pair adds to the middle coefficient :


First NumberSecond NumberSum
1601+60=61
2302+30=32
3203+20=23
4154+15=19
5125+12=17
6106+10=16
-1-60-1+(-60)=-61
-2-30-2+(-30)=-32
-3-20-3+(-20)=-23
-4-15-4+(-15)=-19
-5-12-5+(-12)=-17
-6-10-6+(-10)=-16



From the table, we can see that the two numbers and add to (the middle coefficient).


So the two numbers and both multiply to and add to


Now replace the middle term with . Remember, and add to . So this shows us that .


Replace the second term with .


Group the terms into two pairs.


Factor out the GCF from the first group.


Factor out from the second group. The goal of this step is to make the terms in the second parenthesis equal to the terms in the first parenthesis.


Combine like terms. Or factor out the common term



So factors to .


Note: you can check to see if you did it right by FOILing to get .



So becomes .



Now set each factor equal to zero:


or

or Now solve for t in each case


So our answers are

or

Answer by vleith(2983)   (Show Source): You can put this solution on YOUR website!
Given :

the factor of 5 are 1 and 5. The factors of 12 are 1,12 and 2,6 and 3,4. We need to find the combination that provides a sum or -16.
16 = (2*5 + 1*6)


Using the rule of zero, either one of the other term can be zero and the product is zero. So
Either {{5t - 6 = 0}}} or
Thus
t = 6/5 or t = 2

See this URL --> http://www.hostsrv.com/webmab/app1/MSP/quickmath/02/pageGenerate?site=quickmath&s1=algebra&s2=factor&s3=basic
Note that you must use x as the variable (just use x instead of t)
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