Solve y=z-z/3*(2*z-1)

$$y = z - \frac { z } { 3 } * ( 2 \times z - 1 )$$

Solve for y

$$y=\frac{2z\left(2-z\right)}{3}$$

Solution Steps

Express \frac{z}{3}\left(2z-1\right) as a single fraction.

$$y=z-\frac{z\left(2z-1\right)}{3}$$

Use the distributive property to multiply z by 2z-1.

$$y=z-\frac{2z^{2}-z}{3}$$

Divide each term of 2z^{2}-z by 3 to get \frac{2}{3}z^{2}-\frac{1}{3}z.

$$y=z-\left(\frac{2}{3}z^{2}-\frac{1}{3}z\right)$$

To find the opposite of \frac{2}{3}z^{2}-\frac{1}{3}z, find the opposite of each term.

$$y=z-\frac{2}{3}z^{2}+\frac{1}{3}z$$

Combine z and \frac{1}{3}z to get \frac{4}{3}z.

$$y=\frac{4}{3}z-\frac{2}{3}z^{2}$$

Solve for z (complex solution)

$$z=\frac{\sqrt{4-6y}}{2}+1$$

$$z=-\frac{\sqrt{4-6y}}{2}+1$$

Solve for z

$$z=\frac{\sqrt{4-6y}}{2}+1$$

$$z=-\frac{\sqrt{4-6y}}{2}+1\text{, }y\leq \frac{2}{3}$$