Solve 3v^2*200v-200xleft(v^3+40000right)/left(200vright)^2=0

$$\frac{ 3 { v }^{ 2 } \times 200v-200x \left( { v }^{ 3 } +40000 \right) }{ { \left(200v \right) }^{ 2 } } =0$$

Solve for x

$$x=\frac{3v^{3}}{v^{3}+40000}$$

$$v\neq -20\sqrt[3]{5}\text{ and }v\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 40000v^{2}.

$$3v^{2}\times 200v-200x\left(v^{3}+40000\right)=0$$

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

$$3v^{3}\times 200-200x\left(v^{3}+40000\right)=0$$

Multiply 3 and 200 to get 600.

$$600v^{3}-200x\left(v^{3}+40000\right)=0$$

Use the distributive property to multiply -200x by v^{3}+40000.

$$600v^{3}-200xv^{3}-8000000x=0$$

Subtract 600v^{3} from both sides. Anything subtracted from zero gives its negation.

$$-200xv^{3}-8000000x=-600v^{3}$$

Combine all terms containing x.

$$\left(-200v^{3}-8000000\right)x=-600v^{3}$$

Divide both sides by -200v^{3}-8000000.

$$\frac{\left(-200v^{3}-8000000\right)x}{-200v^{3}-8000000}=-\frac{600v^{3}}{-200v^{3}-8000000}$$

Dividing by -200v^{3}-8000000 undoes the multiplication by -200v^{3}-8000000.

$$x=-\frac{600v^{3}}{-200v^{3}-8000000}$$

Divide -600v^{3} by -200v^{3}-8000000.

$$x=\frac{3v^{3}}{v^{3}+40000}$$

Solve for v

$$v=20\sqrt[3]{\frac{5x}{3-x}}$$

$$x\neq 0\text{ and }x\neq 3$$