Solve 6u=3x^2dx

$$6 u = 3 x ^ { 2 } d x$$

Solve for d (complex solution)

$$\left\{\begin{matrix}d=\frac{2u}{x^{3}}\text{, }&x\neq 0\\d\in \mathrm{C}\text{, }&u=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$6u=3x^{3}d$$

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

$$3x^{3}d=6u$$

Divide both sides by 3x^{3}.

$$\frac{3x^{3}d}{3x^{3}}=\frac{6u}{3x^{3}}$$

Dividing by 3x^{3} undoes the multiplication by 3x^{3}.

$$d=\frac{6u}{3x^{3}}$$

Divide 6u by 3x^{3}.

$$d=\frac{2u}{x^{3}}$$

Solve for d

$$\left\{\begin{matrix}d=\frac{2u}{x^{3}}\text{, }&x\neq 0\\d\in \mathrm{R}\text{, }&u=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$6u=3x^{3}d$$

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

$$3x^{3}d=6u$$

Divide both sides by 3x^{3}.

$$\frac{3x^{3}d}{3x^{3}}=\frac{6u}{3x^{3}}$$

Dividing by 3x^{3} undoes the multiplication by 3x^{3}.

$$d=\frac{6u}{3x^{3}}$$

Divide 6u by 3x^{3}.

$$d=\frac{2u}{x^{3}}$$

Solve for u

$$u=\frac{dx^{3}}{2}$$

Steps for Solving Linear Equation

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$6u=3x^{3}d$$

The equation is in standard form.

$$6u=3dx^{3}$$

Divide both sides by 6.

$$\frac{6u}{6}=\frac{3dx^{3}}{6}$$

Dividing by 6 undoes the multiplication by 6.

$$u=\frac{3dx^{3}}{6}$$

Divide 3x^{3}d by 6.

$$u=\frac{dx^{3}}{2}$$