Solve x^2-(-2x^2)+(-x/2)+x/3

$$x ^ { 2 } - ( - 2 x ^ { 2 } ) + ( - \frac { x } { 2 } ) + \frac { x } { 3 }$$

Evaluate

$$3x^{2}-\frac{x}{6}$$

Solution Steps

The opposite of -2x^{2} is 2x^{2}.

$$x^{2}+2x^{2}-\frac{x}{2}+\frac{x}{3}$$

Combine x^{2} and 2x^{2} to get 3x^{2}.

$$3x^{2}-\frac{x}{2}+\frac{x}{3}$$

Combine -\frac{x}{2} and \frac{x}{3} to get -\frac{1}{6}x.

$$3x^{2}-\frac{1}{6}x$$

Factor

$$\frac{x\left(18x-1\right)}{6}$$

Solution Steps

Factor out \frac{1}{6}.

$$\frac{6x^{2}+12x^{2}-3x+2x}{6}$$

Consider 6x^{2}+12x^{2}-3x+2x. Factor out x.

$$x\left(18x-1\right)$$

Consider 6x+12x-3+2. Multiply and combine like terms.

$$18x-1$$

Rewrite the complete factored expression.

$$\frac{x\left(18x-1\right)}{6}$$