Solve t*4/5(30-4t)*1/2

$$t \cdot \frac { 4 } { 5 } ( 30 - 4 t ) \cdot \frac { 1 } { 2 }$$

Evaluate

$$\frac{4t\left(15-2t\right)}{5}$$

Solution Steps

Multiply \frac{4}{5} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$t\times \frac{4\times 1}{5\times 2}\left(30-4t\right)$$

Do the multiplications in the fraction \frac{4\times 1}{5\times 2}.

$$t\times \frac{4}{10}\left(30-4t\right)$$

Reduce the fraction \frac{4}{10} to lowest terms by extracting and canceling out 2.

$$t\times \frac{2}{5}\left(30-4t\right)$$

Use the distributive property to multiply t\times \frac{2}{5} by 30-4t.

$$t\times \frac{2}{5}\times 30+t\times \frac{2}{5}\left(-4\right)t$$

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

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

Express \frac{2}{5}\times 30 as a single fraction.

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

Multiply 2 and 30 to get 60.

$$t\times \frac{60}{5}+t^{2}\times \frac{2}{5}\left(-4\right)$$

Divide 60 by 5 to get 12.

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

Express \frac{2}{5}\left(-4\right) as a single fraction.

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

Multiply 2 and -4 to get -8.

$$t\times 12+t^{2}\times \frac{-8}{5}$$

Fraction \frac{-8}{5} can be rewritten as -\frac{8}{5} by extracting the negative sign.

$$t\times 12+t^{2}\left(-\frac{8}{5}\right)$$

Expand

$$-\frac{8t^{2}}{5}+12t$$

Solution Steps

Multiply \frac{4}{5} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$t\times \frac{4\times 1}{5\times 2}\left(30-4t\right)$$

Do the multiplications in the fraction \frac{4\times 1}{5\times 2}.

$$t\times \frac{4}{10}\left(30-4t\right)$$

Reduce the fraction \frac{4}{10} to lowest terms by extracting and canceling out 2.

$$t\times \frac{2}{5}\left(30-4t\right)$$

Use the distributive property to multiply t\times \frac{2}{5} by 30-4t.

$$t\times \frac{2}{5}\times 30+t\times \frac{2}{5}\left(-4\right)t$$

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

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

Express \frac{2}{5}\times 30 as a single fraction.

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

Multiply 2 and 30 to get 60.

$$t\times \frac{60}{5}+t^{2}\times \frac{2}{5}\left(-4\right)$$

Divide 60 by 5 to get 12.

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

Express \frac{2}{5}\left(-4\right) as a single fraction.

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

Multiply 2 and -4 to get -8.

$$t\times 12+t^{2}\times \frac{-8}{5}$$

Fraction \frac{-8}{5} can be rewritten as -\frac{8}{5} by extracting the negative sign.

$$t\times 12+t^{2}\left(-\frac{8}{5}\right)$$