Solve ay^2=12y-4

$$a y ^ { 2 } = 12 y - 4$$

Solve for a

$$a=-\frac{4\left(1-3y\right)}{y^{2}}$$

$$y\neq 0$$

Steps for Solving Linear Equation

The equation is in standard form.

$$y^{2}a=12y-4$$

Divide both sides by y^{2}.

$$\frac{y^{2}a}{y^{2}}=\frac{12y-4}{y^{2}}$$

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

$$a=\frac{12y-4}{y^{2}}$$

Divide 12y-4 by y^{2}.

$$a=\frac{4\left(3y-1\right)}{y^{2}}$$

Solve for y (complex solution)

$$\left\{\begin{matrix}y=\frac{2\left(\sqrt{9-a}+3\right)}{a}\text{; }y=\frac{2\left(-\sqrt{9-a}+3\right)}{a}\text{, }&a\neq 0\\y=\frac{1}{3}\text{, }&a=0\end{matrix}\right.$$

Solve for y

$$\left\{\begin{matrix}y=\frac{2\left(\sqrt{9-a}+3\right)}{a}\text{; }y=\frac{2\left(-\sqrt{9-a}+3\right)}{a}\text{, }&a\neq 0\text{ and }a\leq 9\\y=\frac{1}{3}\text{, }&a=0\end{matrix}\right.$$