Solve (3*4/5t)*1/2+1/2*(3/4t+3)*(10-2t)=

$$( 3 \times \frac { 4 } { 5 } t ) \times \frac { 1 } { 2 } + \frac { 1 } { 2 } \times ( \frac { 3 } { 4 } t + 3 ) \times ( 10 - 2 t ) =$$

Evaluate

$$-\frac{3t^{2}}{4}+\frac{39t}{20}+15$$

Solution Steps

Express 3\times \frac{4}{5} as a single fraction.

$$\frac{3\times 4}{5}t\times \frac{1}{2}+\frac{1}{2}\left(\frac{3}{4}t+3\right)\left(10-2t\right)$$

Multiply 3 and 4 to get 12.

$$\frac{12}{5}t\times \frac{1}{2}+\frac{1}{2}\left(\frac{3}{4}t+3\right)\left(10-2t\right)$$

Multiply \frac{12}{5} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{12\times 1}{5\times 2}t+\frac{1}{2}\left(\frac{3}{4}t+3\right)\left(10-2t\right)$$

Do the multiplications in the fraction \frac{12\times 1}{5\times 2}.

$$\frac{12}{10}t+\frac{1}{2}\left(\frac{3}{4}t+3\right)\left(10-2t\right)$$

Reduce the fraction \frac{12}{10} to lowest terms by extracting and canceling out 2.

$$\frac{6}{5}t+\frac{1}{2}\left(\frac{3}{4}t+3\right)\left(10-2t\right)$$

Use the distributive property to multiply \frac{1}{2} by \frac{3}{4}t+3.

$$\frac{6}{5}t+\left(\frac{1}{2}\times \frac{3}{4}t+\frac{1}{2}\times 3\right)\left(10-2t\right)$$

Multiply \frac{1}{2} times \frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{6}{5}t+\left(\frac{1\times 3}{2\times 4}t+\frac{1}{2}\times 3\right)\left(10-2t\right)$$

Do the multiplications in the fraction \frac{1\times 3}{2\times 4}.

$$\frac{6}{5}t+\left(\frac{3}{8}t+\frac{1}{2}\times 3\right)\left(10-2t\right)$$

Multiply \frac{1}{2} and 3 to get \frac{3}{2}.

$$\frac{6}{5}t+\left(\frac{3}{8}t+\frac{3}{2}\right)\left(10-2t\right)$$

Apply the distributive property by multiplying each term of \frac{3}{8}t+\frac{3}{2} by each term of 10-2t.

$$\frac{6}{5}t+\frac{3}{8}t\times 10+\frac{3}{8}t\left(-2\right)t+\frac{3}{2}\times 10+\frac{3}{2}\left(-2\right)t$$

Multiply t and t to get t^{2}.

$$\frac{6}{5}t+\frac{3}{8}t\times 10+\frac{3}{8}t^{2}\left(-2\right)+\frac{3}{2}\times 10+\frac{3}{2}\left(-2\right)t$$

Express \frac{3}{8}\times 10 as a single fraction.

$$\frac{6}{5}t+\frac{3\times 10}{8}t+\frac{3}{8}t^{2}\left(-2\right)+\frac{3}{2}\times 10+\frac{3}{2}\left(-2\right)t$$

Multiply 3 and 10 to get 30.

$$\frac{6}{5}t+\frac{30}{8}t+\frac{3}{8}t^{2}\left(-2\right)+\frac{3}{2}\times 10+\frac{3}{2}\left(-2\right)t$$

Reduce the fraction \frac{30}{8} to lowest terms by extracting and canceling out 2.

$$\frac{6}{5}t+\frac{15}{4}t+\frac{3}{8}t^{2}\left(-2\right)+\frac{3}{2}\times 10+\frac{3}{2}\left(-2\right)t$$

Express \frac{3}{8}\left(-2\right) as a single fraction.

$$\frac{6}{5}t+\frac{15}{4}t+\frac{3\left(-2\right)}{8}t^{2}+\frac{3}{2}\times 10+\frac{3}{2}\left(-2\right)t$$

Multiply 3 and -2 to get -6.

$$\frac{6}{5}t+\frac{15}{4}t+\frac{-6}{8}t^{2}+\frac{3}{2}\times 10+\frac{3}{2}\left(-2\right)t$$

Reduce the fraction \frac{-6}{8} to lowest terms by extracting and canceling out 2.

$$\frac{6}{5}t+\frac{15}{4}t-\frac{3}{4}t^{2}+\frac{3}{2}\times 10+\frac{3}{2}\left(-2\right)t$$

Express \frac{3}{2}\times 10 as a single fraction.

$$\frac{6}{5}t+\frac{15}{4}t-\frac{3}{4}t^{2}+\frac{3\times 10}{2}+\frac{3}{2}\left(-2\right)t$$

Multiply 3 and 10 to get 30.

$$\frac{6}{5}t+\frac{15}{4}t-\frac{3}{4}t^{2}+\frac{30}{2}+\frac{3}{2}\left(-2\right)t$$

Divide 30 by 2 to get 15.

$$\frac{6}{5}t+\frac{15}{4}t-\frac{3}{4}t^{2}+15+\frac{3}{2}\left(-2\right)t$$

Express \frac{3}{2}\left(-2\right) as a single fraction.

$$\frac{6}{5}t+\frac{15}{4}t-\frac{3}{4}t^{2}+15+\frac{3\left(-2\right)}{2}t$$

Multiply 3 and -2 to get -6.

$$\frac{6}{5}t+\frac{15}{4}t-\frac{3}{4}t^{2}+15+\frac{-6}{2}t$$

Divide -6 by 2 to get -3.

$$\frac{6}{5}t+\frac{15}{4}t-\frac{3}{4}t^{2}+15-3t$$

Combine \frac{15}{4}t and -3t to get \frac{3}{4}t.

$$\frac{6}{5}t+\frac{3}{4}t-\frac{3}{4}t^{2}+15$$

Combine \frac{6}{5}t and \frac{3}{4}t to get \frac{39}{20}t.

$$\frac{39}{20}t-\frac{3}{4}t^{2}+15$$

Expand

$$-\frac{3t^{2}}{4}+\frac{39t}{20}+15$$

Solution Steps

Express 3\times \frac{4}{5} as a single fraction.

$$\frac{3\times 4}{5}t\times \frac{1}{2}+\frac{1}{2}\left(\frac{3}{4}t+3\right)\left(10-2t\right)$$

Multiply 3 and 4 to get 12.

$$\frac{12}{5}t\times \frac{1}{2}+\frac{1}{2}\left(\frac{3}{4}t+3\right)\left(10-2t\right)$$

Multiply \frac{12}{5} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{12\times 1}{5\times 2}t+\frac{1}{2}\left(\frac{3}{4}t+3\right)\left(10-2t\right)$$

Do the multiplications in the fraction \frac{12\times 1}{5\times 2}.

$$\frac{12}{10}t+\frac{1}{2}\left(\frac{3}{4}t+3\right)\left(10-2t\right)$$

Reduce the fraction \frac{12}{10} to lowest terms by extracting and canceling out 2.

$$\frac{6}{5}t+\frac{1}{2}\left(\frac{3}{4}t+3\right)\left(10-2t\right)$$

Use the distributive property to multiply \frac{1}{2} by \frac{3}{4}t+3.

$$\frac{6}{5}t+\left(\frac{1}{2}\times \frac{3}{4}t+\frac{1}{2}\times 3\right)\left(10-2t\right)$$

Multiply \frac{1}{2} times \frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{6}{5}t+\left(\frac{1\times 3}{2\times 4}t+\frac{1}{2}\times 3\right)\left(10-2t\right)$$

Do the multiplications in the fraction \frac{1\times 3}{2\times 4}.

$$\frac{6}{5}t+\left(\frac{3}{8}t+\frac{1}{2}\times 3\right)\left(10-2t\right)$$

Multiply \frac{1}{2} and 3 to get \frac{3}{2}.

$$\frac{6}{5}t+\left(\frac{3}{8}t+\frac{3}{2}\right)\left(10-2t\right)$$

Apply the distributive property by multiplying each term of \frac{3}{8}t+\frac{3}{2} by each term of 10-2t.

$$\frac{6}{5}t+\frac{3}{8}t\times 10+\frac{3}{8}t\left(-2\right)t+\frac{3}{2}\times 10+\frac{3}{2}\left(-2\right)t$$

Multiply t and t to get t^{2}.

$$\frac{6}{5}t+\frac{3}{8}t\times 10+\frac{3}{8}t^{2}\left(-2\right)+\frac{3}{2}\times 10+\frac{3}{2}\left(-2\right)t$$

Express \frac{3}{8}\times 10 as a single fraction.

$$\frac{6}{5}t+\frac{3\times 10}{8}t+\frac{3}{8}t^{2}\left(-2\right)+\frac{3}{2}\times 10+\frac{3}{2}\left(-2\right)t$$

Multiply 3 and 10 to get 30.

$$\frac{6}{5}t+\frac{30}{8}t+\frac{3}{8}t^{2}\left(-2\right)+\frac{3}{2}\times 10+\frac{3}{2}\left(-2\right)t$$

Reduce the fraction \frac{30}{8} to lowest terms by extracting and canceling out 2.

$$\frac{6}{5}t+\frac{15}{4}t+\frac{3}{8}t^{2}\left(-2\right)+\frac{3}{2}\times 10+\frac{3}{2}\left(-2\right)t$$

Express \frac{3}{8}\left(-2\right) as a single fraction.

$$\frac{6}{5}t+\frac{15}{4}t+\frac{3\left(-2\right)}{8}t^{2}+\frac{3}{2}\times 10+\frac{3}{2}\left(-2\right)t$$

Multiply 3 and -2 to get -6.

$$\frac{6}{5}t+\frac{15}{4}t+\frac{-6}{8}t^{2}+\frac{3}{2}\times 10+\frac{3}{2}\left(-2\right)t$$

Reduce the fraction \frac{-6}{8} to lowest terms by extracting and canceling out 2.

$$\frac{6}{5}t+\frac{15}{4}t-\frac{3}{4}t^{2}+\frac{3}{2}\times 10+\frac{3}{2}\left(-2\right)t$$

Express \frac{3}{2}\times 10 as a single fraction.

$$\frac{6}{5}t+\frac{15}{4}t-\frac{3}{4}t^{2}+\frac{3\times 10}{2}+\frac{3}{2}\left(-2\right)t$$

Multiply 3 and 10 to get 30.

$$\frac{6}{5}t+\frac{15}{4}t-\frac{3}{4}t^{2}+\frac{30}{2}+\frac{3}{2}\left(-2\right)t$$

Divide 30 by 2 to get 15.

$$\frac{6}{5}t+\frac{15}{4}t-\frac{3}{4}t^{2}+15+\frac{3}{2}\left(-2\right)t$$

Express \frac{3}{2}\left(-2\right) as a single fraction.

$$\frac{6}{5}t+\frac{15}{4}t-\frac{3}{4}t^{2}+15+\frac{3\left(-2\right)}{2}t$$

Multiply 3 and -2 to get -6.

$$\frac{6}{5}t+\frac{15}{4}t-\frac{3}{4}t^{2}+15+\frac{-6}{2}t$$

Divide -6 by 2 to get -3.

$$\frac{6}{5}t+\frac{15}{4}t-\frac{3}{4}t^{2}+15-3t$$

Combine \frac{15}{4}t and -3t to get \frac{3}{4}t.

$$\frac{6}{5}t+\frac{3}{4}t-\frac{3}{4}t^{2}+15$$

Combine \frac{6}{5}t and \frac{3}{4}t to get \frac{39}{20}t.

$$\frac{39}{20}t-\frac{3}{4}t^{2}+15$$