Solve -103847=3*[-393546+60.433*(T-298)]+4*[-241845+51.143*(T-298)]

$$- 103847 = 3 \times [ - 393546 + 60.433 \times ( T - 298 ) ] + 4 \times [ - 241845 + 51.143 \times ( T - 298 ) ]$$

Solve for T

$$T = \frac{93876546}{16777} = 5595\frac{9231}{16777} \approx 5595.55021756$$

Steps for Solving Linear Equation

Use the distributive property to multiply 60.433 by T-298.

$$-103847=3\left(-393546+60.433T-18009.034\right)+4\left(-241845+51.143\left(T-298\right)\right)$$

Subtract 18009.034 from -393546 to get -411555.034.

$$-103847=3\left(-411555.034+60.433T\right)+4\left(-241845+51.143\left(T-298\right)\right)$$

Use the distributive property to multiply 3 by -411555.034+60.433T.

$$-103847=-1234665.102+181.299T+4\left(-241845+51.143\left(T-298\right)\right)$$

Use the distributive property to multiply 51.143 by T-298.

$$-103847=-1234665.102+181.299T+4\left(-241845+51.143T-15240.614\right)$$

Subtract 15240.614 from -241845 to get -257085.614.

$$-103847=-1234665.102+181.299T+4\left(-257085.614+51.143T\right)$$

Use the distributive property to multiply 4 by -257085.614+51.143T.

$$-103847=-1234665.102+181.299T-1028342.456+204.572T$$

Subtract 1028342.456 from -1234665.102 to get -2263007.558.

$$-103847=-2263007.558+181.299T+204.572T$$

Combine 181.299T and 204.572T to get 385.871T.

$$-103847=-2263007.558+385.871T$$

Swap sides so that all variable terms are on the left hand side.

$$-2263007.558+385.871T=-103847$$

Add 2263007.558 to both sides.

$$385.871T=-103847+2263007.558$$

Add -103847 and 2263007.558 to get 2159160.558.

$$385.871T=2159160.558$$

Divide both sides by 385.871.

$$T=\frac{2159160.558}{385.871}$$

Expand \frac{2159160.558}{385.871} by multiplying both numerator and the denominator by 1000.

$$T=\frac{2159160558}{385871}$$

Reduce the fraction \frac{2159160558}{385871} to lowest terms by extracting and canceling out 23.

$$T=\frac{93876546}{16777}$$