Solve 4^2xy^2=2^2dx

$$4 ^ { 2 } x y ^ { 2 } = 2 ^ { 2 } d x$$

Solve for d (complex solution)

$$\left\{\begin{matrix}\\d=4y^{2}\text{, }&\text{unconditionally}\\d\in \mathrm{C}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Calculate 4 to the power of 2 and get 16.

$$16xy^{2}=2^{2}dx$$

Calculate 2 to the power of 2 and get 4.

$$16xy^{2}=4dx$$

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

$$4dx=16xy^{2}$$

The equation is in standard form.

$$4xd=16xy^{2}$$

Divide both sides by 4x.

$$\frac{4xd}{4x}=\frac{16xy^{2}}{4x}$$

Dividing by 4x undoes the multiplication by 4x.

$$d=\frac{16xy^{2}}{4x}$$

Divide 16xy^{2} by 4x.

$$d=4y^{2}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&d=4y^{2}\end{matrix}\right.$$

Steps for Solving Linear Equation

Calculate 4 to the power of 2 and get 16.

$$16xy^{2}=2^{2}dx$$

Calculate 2 to the power of 2 and get 4.

$$16xy^{2}=4dx$$

Subtract 4dx from both sides.

$$16xy^{2}-4dx=0$$

Combine all terms containing x.

$$\left(16y^{2}-4d\right)x=0$$

Divide 0 by 16y^{2}-4d.

$$x=0$$

Solve for d

$$\left\{\begin{matrix}\\d=4y^{2}\text{, }&\text{unconditionally}\\d\in \mathrm{R}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Calculate 4 to the power of 2 and get 16.

$$16xy^{2}=2^{2}dx$$

Calculate 2 to the power of 2 and get 4.

$$16xy^{2}=4dx$$

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

$$4dx=16xy^{2}$$

The equation is in standard form.

$$4xd=16xy^{2}$$

Divide both sides by 4x.

$$\frac{4xd}{4x}=\frac{16xy^{2}}{4x}$$

Dividing by 4x undoes the multiplication by 4x.

$$d=\frac{16xy^{2}}{4x}$$

Divide 16xy^{2} by 4x.

$$d=4y^{2}$$

Solve for x

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&d=4y^{2}\end{matrix}\right.$$

Steps for Solving Linear Equation

Calculate 4 to the power of 2 and get 16.

$$16xy^{2}=2^{2}dx$$

Calculate 2 to the power of 2 and get 4.

$$16xy^{2}=4dx$$

Subtract 4dx from both sides.

$$16xy^{2}-4dx=0$$

Combine all terms containing x.

$$\left(16y^{2}-4d\right)x=0$$

Divide 0 by 16y^{2}-4d.

$$x=0$$