Solve -2a/3+2/2+3a^2/3-3a/2-frac{4a^2}{3}-frac{a}{4}]

$$\frac { - 2 a } { 3 } + \frac { 2 } { 2 } + \frac { 3 a ^ { 2 } } { 3 } - \frac { 3 a } { 2 } - \frac { 4 a ^ { 2 } } { 3 } - \frac { a } { 4 } ]$$

Evaluate

$$-\frac{a^{2}}{3}-\frac{29a}{12}+1$$

Short Solution Steps

Divide 2 by 2 to get 1.

$$\frac{-2a}{3}+1+\frac{3a^{2}}{3}-\frac{3a}{2}-\frac{4a^{2}}{3}-\frac{a}{4}$$

Cancel out 3 and 3.

$$\frac{-2a}{3}+1+a^{2}-\frac{3a}{2}-\frac{4a^{2}}{3}-\frac{a}{4}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1+a^{2} times \frac{3}{3}.

$$\frac{-2a}{3}+\frac{3\left(1+a^{2}\right)}{3}-\frac{3a}{2}-\frac{4a^{2}}{3}-\frac{a}{4}$$

Since \frac{-2a}{3} and \frac{3\left(1+a^{2}\right)}{3} have the same denominator, add them by adding their numerators.

$$\frac{-2a+3\left(1+a^{2}\right)}{3}-\frac{3a}{2}-\frac{4a^{2}}{3}-\frac{a}{4}$$

Do the multiplications in -2a+3\left(1+a^{2}\right).

$$\frac{-2a+3+3a^{2}}{3}-\frac{3a}{2}-\frac{4a^{2}}{3}-\frac{a}{4}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and 2 is 6. Multiply \frac{-2a+3+3a^{2}}{3} times \frac{2}{2}. Multiply \frac{3a}{2} times \frac{3}{3}.

$$\frac{2\left(-2a+3+3a^{2}\right)}{6}-\frac{3\times 3a}{6}-\frac{4a^{2}}{3}-\frac{a}{4}$$

Since \frac{2\left(-2a+3+3a^{2}\right)}{6} and \frac{3\times 3a}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2\left(-2a+3+3a^{2}\right)-3\times 3a}{6}-\frac{4a^{2}}{3}-\frac{a}{4}$$

Do the multiplications in 2\left(-2a+3+3a^{2}\right)-3\times 3a.

$$\frac{-4a+6+6a^{2}-9a}{6}-\frac{4a^{2}}{3}-\frac{a}{4}$$

Combine like terms in -4a+6+6a^{2}-9a.

$$\frac{-13a+6+6a^{2}}{6}-\frac{4a^{2}}{3}-\frac{a}{4}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 6 and 3 is 6. Multiply \frac{4a^{2}}{3} times \frac{2}{2}.

$$\frac{-13a+6+6a^{2}}{6}-\frac{2\times 4a^{2}}{6}-\frac{a}{4}$$

Since \frac{-13a+6+6a^{2}}{6} and \frac{2\times 4a^{2}}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-13a+6+6a^{2}-2\times 4a^{2}}{6}-\frac{a}{4}$$

Do the multiplications in -13a+6+6a^{2}-2\times 4a^{2}.

$$\frac{-13a+6+6a^{2}-8a^{2}}{6}-\frac{a}{4}$$

Combine like terms in -13a+6+6a^{2}-8a^{2}.

$$\frac{-13a+6-2a^{2}}{6}-\frac{a}{4}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 6 and 4 is 12. Multiply \frac{-13a+6-2a^{2}}{6} times \frac{2}{2}. Multiply \frac{a}{4} times \frac{3}{3}.

$$\frac{2\left(-13a+6-2a^{2}\right)}{12}-\frac{3a}{12}$$

Since \frac{2\left(-13a+6-2a^{2}\right)}{12} and \frac{3a}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2\left(-13a+6-2a^{2}\right)-3a}{12}$$

Do the multiplications in 2\left(-13a+6-2a^{2}\right)-3a.

$$\frac{-26a+12-4a^{2}-3a}{12}$$

Combine like terms in -26a+12-4a^{2}-3a.

$$\frac{-29a+12-4a^{2}}{12}$$

Factor

$$-\frac{1}{3}\left(a-\frac{-\sqrt{1033}-29}{8}\right)\left(a-\frac{\sqrt{1033}-29}{8}\right)$$