Solve P(n2)/C(n+12)=3/2

$$\frac { P ( n 2 ) } { C ( n + 12 ) } = \frac { 3 } { 2 }$$

Solve for C

$$C=\frac{2Pn_{2}}{3\left(n+12\right)}$$

$$n\neq -12\text{ and }n_{2}\neq 0\text{ and }P\neq 0$$

Steps for Solving Linear Equation

Variable C cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 2C\left(n+12\right), the least common multiple of C\left(n+12\right),2.

$$2Pn_{2}=3C\left(n+12\right)$$

Use the distributive property to multiply 3C by n+12.

$$2Pn_{2}=3Cn+36C$$

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

$$3Cn+36C=2Pn_{2}$$

Combine all terms containing C.

$$\left(3n+36\right)C=2Pn_{2}$$

Divide both sides by 3n+36.

$$\frac{\left(3n+36\right)C}{3n+36}=\frac{2Pn_{2}}{3n+36}$$

Dividing by 3n+36 undoes the multiplication by 3n+36.

$$C=\frac{2Pn_{2}}{3n+36}$$

Divide 2Pn_{2} by 3n+36.

$$C=\frac{2Pn_{2}}{3\left(n+12\right)}$$

Variable C cannot be equal to 0.

$$C=\frac{2Pn_{2}}{3\left(n+12\right)}\text{, }C\neq 0$$

Solve for P

$$P=\frac{3C\left(n+12\right)}{2n_{2}}$$

$$n_{2}\neq 0\text{ and }C\neq 0\text{ and }n\neq -12$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2C\left(n+12\right), the least common multiple of C\left(n+12\right),2.

$$2Pn_{2}=3C\left(n+12\right)$$

Use the distributive property to multiply 3C by n+12.

$$2Pn_{2}=3Cn+36C$$

The equation is in standard form.

$$2n_{2}P=3Cn+36C$$

Divide both sides by 2n_{2}.

$$\frac{2n_{2}P}{2n_{2}}=\frac{3C\left(n+12\right)}{2n_{2}}$$

Dividing by 2n_{2} undoes the multiplication by 2n_{2}.

$$P=\frac{3C\left(n+12\right)}{2n_{2}}$$