Solve x^2-x^2-1+2x+2x^2+4/3x-2/3x-4/9

$${ x }^{ 2 } - { x }^{ 2 } -1+2x+2 { x }^{ 2 } + \frac{ 4 }{ 3 } x- \frac{ 2 }{ 3 } x- \frac{ 4 }{ 9 }$$

Evaluate

$$2x^{2}+\frac{8x}{3}-\frac{13}{9}$$

Solution Steps

Combine x^{2} and -x^{2} to get 0.

$$-1+2x+2x^{2}+\frac{4}{3}x-\frac{2}{3}x-\frac{4}{9}$$

Combine 2x and \frac{4}{3}x to get \frac{10}{3}x.

$$-1+\frac{10}{3}x+2x^{2}-\frac{2}{3}x-\frac{4}{9}$$

Combine \frac{10}{3}x and -\frac{2}{3}x to get \frac{8}{3}x.

$$-1+\frac{8}{3}x+2x^{2}-\frac{4}{9}$$

Subtract \frac{4}{9} from -1 to get -\frac{13}{9}.

$$-\frac{13}{9}+\frac{8}{3}x+2x^{2}$$

Factor

$$2\left(x-\left(-\frac{\sqrt{42}}{6}-\frac{2}{3}\right)\right)\left(x-\left(\frac{\sqrt{42}}{6}-\frac{2}{3}\right)\right)$$