Solve -2/7-3/5w^2+2/3+2/5w^2-frac{3}{5}+frac{3}{7}w-frac{62}{3}=

$$- \frac { 2 } { 7 } - \frac { 3 } { 5 } w ^ { 2 } + \frac { 2 } { 3 } + \frac { 2 } { 5 } w ^ { 2 } - \frac { 3 } { 5 } + \frac { 3 } { 7 } w - \frac { 62 } { 3 } =$$

Evaluate

$$-\frac{w^{2}}{5}+\frac{3w}{7}-\frac{731}{35}$$

Solution Steps

Add -\frac{2}{7} and \frac{2}{3} to get \frac{8}{21}.

$$\frac{8}{21}-\frac{3}{5}w^{2}+\frac{2}{5}w^{2}-\frac{3}{5}+\frac{3}{7}w-\frac{62}{3}$$

Combine -\frac{3}{5}w^{2} and \frac{2}{5}w^{2} to get -\frac{1}{5}w^{2}.

$$\frac{8}{21}-\frac{1}{5}w^{2}-\frac{3}{5}+\frac{3}{7}w-\frac{62}{3}$$

Subtract \frac{3}{5} from \frac{8}{21} to get -\frac{23}{105}.

$$-\frac{23}{105}-\frac{1}{5}w^{2}+\frac{3}{7}w-\frac{62}{3}$$

Subtract \frac{62}{3} from -\frac{23}{105} to get -\frac{731}{35}.

$$-\frac{731}{35}-\frac{1}{5}w^{2}+\frac{3}{7}w$$

Factor

$$\frac{-7w^{2}+15w-731}{35}$$

Solution Steps

Factor out \frac{1}{105}.

$$\frac{-2193-21w^{2}+45w}{105}$$

Consider -30-63w^{2}+70+42w^{2}-63+45w-2170. Multiply and combine like terms.

$$-21w^{2}+45w-2193$$

Consider -21w^{2}+45w-2193. Factor out 3.

$$3\left(-7w^{2}+15w-731\right)$$

Rewrite the complete factored expression.

$$\frac{-7w^{2}+15w-731}{35}$$