Solve y^2-(3m-2)y+1=0

$$y ^ { 2 } - ( 3 m - 2 ) y + 1 = 0$$

Solve for m

$$m=\frac{\left(y+1\right)^{2}}{3y}$$

$$y\neq 0$$

Steps for Solving Linear Equation

Use the distributive property to multiply 3m-2 by y.

$$y^{2}-\left(3my-2y\right)+1=0$$

To find the opposite of 3my-2y, find the opposite of each term.

$$y^{2}-3my+2y+1=0$$

Subtract y^{2} from both sides. Anything subtracted from zero gives its negation.

$$-3my+2y+1=-y^{2}$$

Subtract 2y from both sides.

$$-3my+1=-y^{2}-2y$$

Subtract 1 from both sides.

$$-3my=-y^{2}-2y-1$$

The equation is in standard form.

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

Divide both sides by -3y.

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

Dividing by -3y undoes the multiplication by -3y.

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

Divide -\left(y+1\right)^{2} by -3y.

$$m=\frac{\left(y+1\right)^{2}}{3y}$$

Solve for y (complex solution)

$$y=\frac{\sqrt{9m^{2}-12m}}{2}+\frac{3m}{2}-1$$

$$y=-\frac{\sqrt{9m^{2}-12m}}{2}+\frac{3m}{2}-1$$

Solve for y

$$y=\frac{\sqrt{9m^{2}-12m}}{2}+\frac{3m}{2}-1$$

$$y=-\frac{\sqrt{9m^{2}-12m}}{2}+\frac{3m}{2}-1\text{, }m\geq \frac{4}{3}\text{ or }m\leq 0$$