Solve y=-4x^2w

$$y = - 4 x ^ { 2 } w$$

Solve for w (complex solution)

$$\left\{\begin{matrix}w=-\frac{y}{4x^{2}}\text{, }&x\neq 0\\w\in \mathrm{C}\text{, }&y=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$-4x^{2}w=y$$

The equation is in standard form.

$$\left(-4x^{2}\right)w=y$$

Divide both sides by -4x^{2}.

$$\frac{\left(-4x^{2}\right)w}{-4x^{2}}=\frac{y}{-4x^{2}}$$

Dividing by -4x^{2} undoes the multiplication by -4x^{2}.

$$w=\frac{y}{-4x^{2}}$$

Divide y by -4x^{2}.

$$w=-\frac{y}{4x^{2}}$$

Solve for w

$$\left\{\begin{matrix}w=-\frac{y}{4x^{2}}\text{, }&x\neq 0\\w\in \mathrm{R}\text{, }&y=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$-4x^{2}w=y$$

The equation is in standard form.

$$\left(-4x^{2}\right)w=y$$

Divide both sides by -4x^{2}.

$$\frac{\left(-4x^{2}\right)w}{-4x^{2}}=\frac{y}{-4x^{2}}$$

Dividing by -4x^{2} undoes the multiplication by -4x^{2}.

$$w=\frac{y}{-4x^{2}}$$

Divide y by -4x^{2}.

$$w=-\frac{y}{4x^{2}}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=-\frac{iw^{-\frac{1}{2}}\sqrt{y}}{2}\text{; }x=\frac{iw^{-\frac{1}{2}}\sqrt{y}}{2}\text{, }&w\neq 0\\x\in \mathrm{C}\text{, }&y=0\text{ and }w=0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\frac{\sqrt{-\frac{y}{w}}}{2}\text{; }x=-\frac{\sqrt{-\frac{y}{w}}}{2}\text{, }&\left(w>0\text{ and }y\leq 0\right)\text{ or }\left(y\geq 0\text{ and }w<0\right)\\x\in \mathrm{R}\text{, }&y=0\text{ and }w=0\end{matrix}\right.$$