Solve am^2-3m+3=1

$$a m ^ { 2 } - 3 m + 3 = 1$$

Solve for a

$$a=-\frac{2-3m}{m^{2}}$$

$$m\neq 0$$

Steps for Solving Linear Equation

Add 3m to both sides.

$$am^{2}+3=1+3m$$

Subtract 3 from both sides.

$$am^{2}=1+3m-3$$

Subtract 3 from 1 to get -2.

$$am^{2}=-2+3m$$

The equation is in standard form.

$$m^{2}a=3m-2$$

Divide both sides by m^{2}.

$$\frac{m^{2}a}{m^{2}}=\frac{3m-2}{m^{2}}$$

Dividing by m^{2} undoes the multiplication by m^{2}.

$$a=\frac{3m-2}{m^{2}}$$

Solve for m (complex solution)

$$\left\{\begin{matrix}m=\frac{\sqrt{9-8a}+3}{2a}\text{; }m=\frac{-\sqrt{9-8a}+3}{2a}\text{, }&a\neq 0\\m=\frac{2}{3}\text{, }&a=0\end{matrix}\right.$$

Solve for m

$$\left\{\begin{matrix}m=\frac{\sqrt{9-8a}+3}{2a}\text{; }m=\frac{-\sqrt{9-8a}+3}{2a}\text{, }&a\neq 0\text{ and }a\leq \frac{9}{8}\\m=\frac{2}{3}\text{, }&a=0\end{matrix}\right.$$