Solve -4t-4t/15+6+2/3=

$$- 4 t - \frac { 4 t } { 15 } + 6 + 2 / 3 =$$

Evaluate

$$-\frac{64t}{15}+\frac{20}{3}$$

Short Solution Steps

Convert 6 to fraction \frac{18}{3}.

$$-4t-\frac{4t}{15}+\frac{18}{3}+\frac{2}{3}$$

Since \frac{18}{3} and \frac{2}{3} have the same denominator, add them by adding their numerators.

$$-4t-\frac{4t}{15}+\frac{18+2}{3}$$

Add 18 and 2 to get 20.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 15 and 3 is 15. Multiply \frac{20}{3} times \frac{5}{5}.

$$-4t-\frac{4t}{15}+\frac{20\times 5}{15}$$

Since -\frac{4t}{15} and \frac{20\times 5}{15} have the same denominator, add them by adding their numerators.

$$-4t+\frac{-4t+20\times 5}{15}$$

Do the multiplications in -4t+20\times 5.

$$-4t+\frac{-4t+100}{15}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -4t times \frac{15}{15}.

$$\frac{15\left(-4\right)t}{15}+\frac{-4t+100}{15}$$

Since \frac{15\left(-4\right)t}{15} and \frac{-4t+100}{15} have the same denominator, add them by adding their numerators.

$$\frac{15\left(-4\right)t-4t+100}{15}$$

Do the multiplications in 15\left(-4\right)t-4t+100.

$$\frac{-60t-4t+100}{15}$$

Combine like terms in -60t-4t+100.

$$\frac{-64t+100}{15}$$

Factor

$$\frac{4\left(25-16t\right)}{15}$$

Solution Steps

Factor out \frac{2}{15}.

$$\frac{2\left(-32t+50\right)}{15}$$

Consider -30t-2t+45+5. Multiply and combine like terms.

$$-32t+50$$

Consider -32t+50. Factor out 2.

$$2\left(-16t+25\right)$$

Rewrite the complete factored expression.

$$\frac{4\left(-16t+25\right)}{15}$$