Solve w^2-2/7-2/5-3/5w^2+2/3+frac{2}{5}w^2-frac{3}{5}+frac{3}{7}w-frac{4}{3}=

$$w ^ { 2 } - \frac { 2 } { 7 } - \frac { 2 } { 5 } - \frac { 3 } { 5 } w ^ { 2 } + \frac { 2 } { 3 } + \frac { 2 } { 5 } w ^ { 2 } - \frac { 3 } { 5 } + \frac { 3 } { 7 } w - \frac { 4 } { 3 } =$$

Evaluate

$$\frac{4w^{2}}{5}+\frac{3w}{7}-\frac{41}{21}$$

Solution Steps

Subtract \frac{2}{5} from -\frac{2}{7} to get -\frac{24}{35}.

$$w^{2}-\frac{24}{35}-\frac{3}{5}w^{2}+\frac{2}{3}+\frac{2}{5}w^{2}-\frac{3}{5}+\frac{3}{7}w-\frac{4}{3}$$

Combine w^{2} and -\frac{3}{5}w^{2} to get \frac{2}{5}w^{2}.

$$\frac{2}{5}w^{2}-\frac{24}{35}+\frac{2}{3}+\frac{2}{5}w^{2}-\frac{3}{5}+\frac{3}{7}w-\frac{4}{3}$$

Add -\frac{24}{35} and \frac{2}{3} to get -\frac{2}{105}.

$$\frac{2}{5}w^{2}-\frac{2}{105}+\frac{2}{5}w^{2}-\frac{3}{5}+\frac{3}{7}w-\frac{4}{3}$$

Combine \frac{2}{5}w^{2} and \frac{2}{5}w^{2} to get \frac{4}{5}w^{2}.

$$\frac{4}{5}w^{2}-\frac{2}{105}-\frac{3}{5}+\frac{3}{7}w-\frac{4}{3}$$

Subtract \frac{3}{5} from -\frac{2}{105} to get -\frac{13}{21}.

$$\frac{4}{5}w^{2}-\frac{13}{21}+\frac{3}{7}w-\frac{4}{3}$$

Subtract \frac{4}{3} from -\frac{13}{21} to get -\frac{41}{21}.

$$\frac{4}{5}w^{2}-\frac{41}{21}+\frac{3}{7}w$$

Factor

$$\frac{4\left(w-\left(-\frac{\sqrt{70905}}{168}-\frac{15}{56}\right)\right)\left(w-\left(\frac{\sqrt{70905}}{168}-\frac{15}{56}\right)\right)}{5}$$