SOLUTION: I have a problem where I need to solve the equation (2/t)= (t/5t-12) and the lcd will be 5t-12, but the answers that I come up with when I work this problem have not matched the

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Question 188130This question is from textbook
: I have a problem where I need to solve the equation
(2/t)= (t/5t-12)
and the lcd will be 5t-12, but the answers that I come up with when I work this problem have not matched the answers in the back of the book so far. I think the issue I'm having is when i do the 2/t it seems to me that teh t's will cancel and then I am left with 10-24, but that seems to not work
Any help with this would be greatly appreciated!! This question is from textbook

Found 2 solutions by stanbon, ankor@dixie-net.com:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
solve the equation
(2/t)= (t/5t-12)
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Cross-multiply to get:
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2(5t-12) = t^2
10t - 24 = t^2
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Rearrange:
t^2 - 10t + 24 = 0
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Factor
(t-6)(t-4) = 0
t = 6 or t = 4
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Another way to do it without cross-multiplying:
(2/t)= (t/5t-12)
The least common multiplier of the denominators is t(5t-12)
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multiply both sides by the lcm to get:
(2)(5t-12)= (t)(t)
10t -24 = t^2
t^2 -10t + 24 = 0
(t-6)(t-4)
t = 6or t = 4
===================
Cheers,
Stan H.
Cheers,
Stan H.

Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
=
Cross multiply
2(5t-12) = t^2
:
10t - 24 = t^2
:
0 = t^2 - 10t + 24
A quadratic equation that can be factored to:
(t-4)(t-6) = 0
two solutions:
t = +4
and
t = +6
:
:
Check both solutions in original problem
x=6
=
=
=
You can check solution x=4 in the same way