Solve 15w/18cm=4m/x+2

$$\frac { 15 w } { 18 c m } = \frac { 4 m } { x + 2 }$$

Solve for c

$$c=\frac{5w\left(x+2\right)}{24m^{2}}$$

$$m\neq 0\text{ and }w\neq 0\text{ and }x\neq -2$$

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 18cm\left(x+2\right), the least common multiple of 18cm,x+2.

$$\left(x+2\right)\times 15w=18cm\times 4m$$

Use the distributive property to multiply x+2 by 15.

$$\left(15x+30\right)w=18cm\times 4m$$

Use the distributive property to multiply 15x+30 by w.

$$15xw+30w=18cm\times 4m$$

Multiply m and m to get m^{2}.

$$15xw+30w=18cm^{2}\times 4$$

Multiply 18 and 4 to get 72.

$$15xw+30w=72cm^{2}$$

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

$$72cm^{2}=15xw+30w$$

The equation is in standard form.

$$72m^{2}c=15wx+30w$$

Divide both sides by 72m^{2}.

$$\frac{72m^{2}c}{72m^{2}}=\frac{15w\left(x+2\right)}{72m^{2}}$$

Dividing by 72m^{2} undoes the multiplication by 72m^{2}.

$$c=\frac{15w\left(x+2\right)}{72m^{2}}$$

Divide 15w\left(2+x\right) by 72m^{2}.

$$c=\frac{5w\left(x+2\right)}{24m^{2}}$$

Variable c cannot be equal to 0.

$$c=\frac{5w\left(x+2\right)}{24m^{2}}\text{, }c\neq 0$$

Solve for m (complex solution)

$$m=-\frac{c^{-\frac{1}{2}}\sqrt{w}\sqrt{30\left(x+2\right)}}{12}$$

$$m=\frac{c^{-\frac{1}{2}}\sqrt{w}\sqrt{30\left(x+2\right)}}{12}\text{, }x\neq -2\text{ and }w\neq 0\text{ and }c\neq 0$$

Solve for m

$$m=\frac{\sqrt{\frac{30w\left(x+2\right)}{c}}}{12}$$

$$m=-\frac{\sqrt{\frac{30w\left(x+2\right)}{c}}}{12}\text{, }\left(c<0\text{ and }x<-2\text{ and }w>0\right)\text{ or }\left(c<0\text{ and }w<0\text{ and }x>-2\right)\text{ or }\left(c>0\text{ and }w>0\text{ and }x>-2\right)\text{ or }\left(c>0\text{ and }x<-2\text{ and }w<0\right)$$