Solve 1080+3t-25*38/4/145-5*5^2=6.5

$$\frac { 1080 + 3 t - 25 \times \frac { 38 } { 4 } } { 145 - 5 \times 5 ^ { 2 } } = 6.5$$

Solve for t

$$t=-237.5$$

Steps for Solving Linear Equation

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\frac{1080+3t-25\times \frac{38}{4}}{145-5^{3}}=6.5$$

Reduce the fraction \frac{38}{4} to lowest terms by extracting and canceling out 2.

$$\frac{1080+3t-25\times \frac{19}{2}}{145-5^{3}}=6.5$$

Express 25\times \frac{19}{2} as a single fraction.

$$\frac{1080+3t-\frac{25\times 19}{2}}{145-5^{3}}=6.5$$

Multiply 25 and 19 to get 475.

$$\frac{1080+3t-\frac{475}{2}}{145-5^{3}}=6.5$$

Convert 1080 to fraction \frac{2160}{2}.

$$\frac{\frac{2160}{2}+3t-\frac{475}{2}}{145-5^{3}}=6.5$$

Since \frac{2160}{2} and \frac{475}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{2160-475}{2}+3t}{145-5^{3}}=6.5$$

Subtract 475 from 2160 to get 1685.

$$\frac{\frac{1685}{2}+3t}{145-5^{3}}=6.5$$

Calculate 5 to the power of 3 and get 125.

$$\frac{\frac{1685}{2}+3t}{145-125}=6.5$$

Subtract 125 from 145 to get 20.

$$\frac{\frac{1685}{2}+3t}{20}=6.5$$

Divide each term of \frac{1685}{2}+3t by 20 to get \frac{337}{8}+\frac{3}{20}t.

$$\frac{337}{8}+\frac{3}{20}t=6.5$$

Subtract \frac{337}{8} from both sides.

$$\frac{3}{20}t=6.5-\frac{337}{8}$$

Convert decimal number 6.5 to fraction \frac{65}{10}. Reduce the fraction \frac{65}{10} to lowest terms by extracting and canceling out 5.

$$\frac{3}{20}t=\frac{13}{2}-\frac{337}{8}$$

Least common multiple of 2 and 8 is 8. Convert \frac{13}{2} and \frac{337}{8} to fractions with denominator 8.

$$\frac{3}{20}t=\frac{52}{8}-\frac{337}{8}$$

Since \frac{52}{8} and \frac{337}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3}{20}t=\frac{52-337}{8}$$

Subtract 337 from 52 to get -285.

$$\frac{3}{20}t=-\frac{285}{8}$$

Multiply both sides by \frac{20}{3}, the reciprocal of \frac{3}{20}.

$$t=-\frac{285}{8}\times \frac{20}{3}$$

Multiply -\frac{285}{8} times \frac{20}{3} by multiplying numerator times numerator and denominator times denominator.

$$t=\frac{-285\times 20}{8\times 3}$$

Do the multiplications in the fraction \frac{-285\times 20}{8\times 3}.

$$t=\frac{-5700}{24}$$

Reduce the fraction \frac{-5700}{24} to lowest terms by extracting and canceling out 12.

$$t=-\frac{475}{2}$$