Solve bx+c/3a=y^2

$$\frac { b x + c } { 3 a } = y ^ { 2 }$$

Solve for b (complex solution)

$$\left\{\begin{matrix}b=-\frac{c-3ay^{2}}{x}\text{, }&x\neq 0\text{ and }a\neq 0\\b\in \mathrm{C}\text{, }&c=3ay^{2}\text{ and }x=0\text{ and }a\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 3a.

$$bx+c=3ay^{2}$$

Subtract c from both sides.

$$bx=3ay^{2}-c$$

The equation is in standard form.

$$xb=3ay^{2}-c$$

Divide both sides by x.

$$\frac{xb}{x}=\frac{3ay^{2}-c}{x}$$

Dividing by x undoes the multiplication by x.

$$b=\frac{3ay^{2}-c}{x}$$

Solve for a

$$\left\{\begin{matrix}a=\frac{bx+c}{3y^{2}}\text{, }&\left(c\neq 0\text{ or }x\neq 0\right)\text{ and }\left(x=0\text{ or }b\neq -\frac{c}{x}\right)\text{ and }\left(b\neq 0\text{ or }c\neq 0\right)\text{ and }y\neq 0\text{ and }c\neq -bx\\a\neq 0\text{, }&y=0\text{ and }c=-bx\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable a cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 3a.

$$bx+c=3ay^{2}$$

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

$$3ay^{2}=bx+c$$

The equation is in standard form.

$$3y^{2}a=bx+c$$

Divide both sides by 3y^{2}.

$$\frac{3y^{2}a}{3y^{2}}=\frac{bx+c}{3y^{2}}$$

Dividing by 3y^{2} undoes the multiplication by 3y^{2}.

$$a=\frac{bx+c}{3y^{2}}$$

Variable a cannot be equal to 0.

$$a=\frac{bx+c}{3y^{2}}\text{, }a\neq 0$$

Solve for b

$$\left\{\begin{matrix}b=-\frac{c-3ay^{2}}{x}\text{, }&x\neq 0\text{ and }a\neq 0\\b\in \mathrm{R}\text{, }&c=3ay^{2}\text{ and }x=0\text{ and }a\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 3a.

$$bx+c=3ay^{2}$$

Subtract c from both sides.

$$bx=3ay^{2}-c$$

The equation is in standard form.

$$xb=3ay^{2}-c$$

Divide both sides by x.

$$\frac{xb}{x}=\frac{3ay^{2}-c}{x}$$

Dividing by x undoes the multiplication by x.

$$b=\frac{3ay^{2}-c}{x}$$