Solve {l}{(2/3)^2-4*a*2/3}{+2*2/3+6*a-3}

$$\left. \begin{array} { l } { ( \frac { 2 } { 3 } ) ^ { 2 } - 4 \cdot a \cdot \frac { 2 } { 3 } } \\ { + 2 \cdot \frac { 2 } { 3 } + 6 \cdot a - 3 } \end{array} \right.$$

Evaluate

$$\frac{10a}{3}-\frac{11}{9}$$

Solution Steps

Calculate \frac{2}{3} to the power of 2 and get \frac{4}{9}.

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

Express 4\times \frac{2}{3} as a single fraction.

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

Multiply 4 and 2 to get 8.

$$\frac{4}{9}-\frac{8}{3}a+2\times \frac{2}{3}+6a-3$$

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

$$\frac{4}{9}-\frac{8}{3}a+\frac{2\times 2}{3}+6a-3$$

Multiply 2 and 2 to get 4.

$$\frac{4}{9}-\frac{8}{3}a+\frac{4}{3}+6a-3$$

Least common multiple of 9 and 3 is 9. Convert \frac{4}{9} and \frac{4}{3} to fractions with denominator 9.

$$\frac{4}{9}-\frac{8}{3}a+\frac{12}{9}+6a-3$$

Since \frac{4}{9} and \frac{12}{9} have the same denominator, add them by adding their numerators.

$$\frac{4+12}{9}-\frac{8}{3}a+6a-3$$

Add 4 and 12 to get 16.

$$\frac{16}{9}-\frac{8}{3}a+6a-3$$

Combine -\frac{8}{3}a and 6a to get \frac{10}{3}a.

$$\frac{16}{9}+\frac{10}{3}a-3$$

Convert 3 to fraction \frac{27}{9}.

$$\frac{16}{9}+\frac{10}{3}a-\frac{27}{9}$$

Since \frac{16}{9} and \frac{27}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{16-27}{9}+\frac{10}{3}a$$

Subtract 27 from 16 to get -11.

$$-\frac{11}{9}+\frac{10}{3}a$$

Factor

$$\frac{30a-11}{9}$$

Solution Steps

Factor out \frac{1}{9}.

$$\frac{-11+30a}{9}$$

Consider 4-24a+12+54a-27. Multiply and combine like terms.

$$30a-11$$

Rewrite the complete factored expression.

$$\frac{30a-11}{9}$$