Solve y=kx^2+12x+36

$$y = k x ^ { 2 } + 12 x + 36$$

Solve for k (complex solution)

$$\left\{\begin{matrix}k=-\frac{12x-y+36}{x^{2}}\text{, }&x\neq 0\\k\in \mathrm{C}\text{, }&y=36\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$kx^{2}+12x+36=y$$

Subtract 12x from both sides.

$$kx^{2}+36=y-12x$$

Subtract 36 from both sides.

$$kx^{2}=y-12x-36$$

The equation is in standard form.

$$x^{2}k=-12x+y-36$$

Divide both sides by x^{2}.

$$\frac{x^{2}k}{x^{2}}=\frac{-12x+y-36}{x^{2}}$$

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

$$k=\frac{-12x+y-36}{x^{2}}$$

Solve for k

$$\left\{\begin{matrix}k=-\frac{12x-y+36}{x^{2}}\text{, }&x\neq 0\\k\in \mathrm{R}\text{, }&y=36\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$kx^{2}+12x+36=y$$

Subtract 12x from both sides.

$$kx^{2}+36=y-12x$$

Subtract 36 from both sides.

$$kx^{2}=y-12x-36$$

The equation is in standard form.

$$x^{2}k=-12x+y-36$$

Divide both sides by x^{2}.

$$\frac{x^{2}k}{x^{2}}=\frac{-12x+y-36}{x^{2}}$$

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

$$k=\frac{-12x+y-36}{x^{2}}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{ky-36k+36}-6}{k}\text{; }x=-\frac{\sqrt{ky-36k+36}+6}{k}\text{, }&k\neq 0\\x=\frac{y-36}{12}\text{, }&k=0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\frac{\sqrt{ky-36k+36}-6}{k}\text{; }x=-\frac{\sqrt{ky-36k+36}+6}{k}\text{, }&\left(k>0\text{ or }y\leq -\frac{36-36k}{k}\right)\text{ and }\left(y\leq \text{Indeterminate}\text{ or }k\neq 0\right)\text{ and }\left(k<0\text{ or }\left(k\neq 0\text{ and }y\geq -\frac{36-36k}{k}\right)\right)\\x=\frac{y-36}{12}\text{, }&k=0\end{matrix}\right.$$