Solve a^2-3ay=a(a-3b)

$$a ^ { 2 } - 3 a y = a ( a - 3 b )$$

Solve for a

$$\left\{\begin{matrix}\\a=0\text{, }&\text{unconditionally}\\a\in \mathrm{R}\text{, }&y=b\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply a by a-3b.

$$a^{2}-3ay=a^{2}-3ab$$

Subtract a^{2} from both sides.

$$a^{2}-3ay-a^{2}=-3ab$$

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

$$-3ay=-3ab$$

Add 3ab to both sides.

$$-3ay+3ab=0$$

Combine all terms containing a.

$$\left(-3y+3b\right)a=0$$

The equation is in standard form.

$$\left(3b-3y\right)a=0$$

Divide 0 by -3y+3b.

$$a=0$$

Solve for b

$$\left\{\begin{matrix}\\b=y\text{, }&\text{unconditionally}\\b\in \mathrm{R}\text{, }&a=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply a by a-3b.

$$a^{2}-3ay=a^{2}-3ab$$

Swap sides so that all variable terms are on the left hand side.

$$a^{2}-3ab=a^{2}-3ay$$

Subtract a^{2} from both sides.

$$-3ab=a^{2}-3ay-a^{2}$$

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

$$-3ab=-3ay$$

Cancel out -3 on both sides.

$$ab=ay$$

Divide both sides by a.

$$\frac{ab}{a}=\frac{ay}{a}$$

Dividing by a undoes the multiplication by a.

$$b=\frac{ay}{a}$$

Divide ay by a.

$$b=y$$