Obtaining an algebraic Equation for T

(0.300)(4190J/(kg*K)(T-70.0*C) +
(0.100)(390J)/(kg*K)(T-20.0*C)

I don't know how to use the Algebraic Equation on that?

suppressing all those units, we have

(.300)(4190)(T-70) + (.100)(390)(T-20)
= 1257T - 87990 + 39T-780
= 1296T - 88770

You can do with that what you will

To obtain the algebraic equation for T, we can simplify and rearrange the equation given. Let's break it down step by step:

1. Start with the given equation:
(0.300)(4190J/(kg*K)(T-70.0*C) + (0.100)(390J)/(kg*K)(T-20.0*C).

2. Simplify each term:
(0.300)(4190J/(kg*K)(T-70.0*C) = 1257J/(kg*K)(T-70.0*C)
(0.100)(390J)/(kg*K)(T-20.0*C) = 39J/(kg*K)(T-20.0*C)

3. Combine the two simplified terms:
1257J/(kg*K)(T-70.0*C) + 39J/(kg*K)(T-20.0*C).

4. Find a common denominator:
The denominators, (T-70.0*C) and (T-20.0*C), are the same, so no need to find the common denominator.

5. Add the numerators while keeping the denominator the same:
1257J + 39J / (kg*K)(T-20.0*C).

6. Combine like terms in the numerator:
1296J / (kg*K)(T-20.0*C).

7. Finally, we have the simplified equation for T:
(1296J) / ((kg*K)(T-20.0*C)) = T.

So, the simplified algebraic equation for T is T = (1296J) / ((kg*K)(T-20.0*C)).