Solve 2m/3n^2=4t^2/5w

$$\frac { 2 m } { 3 n ^ { 2 } } = \frac { 4 t ^ { 2 } } { 5 w }$$

Solve for m

$$m=\frac{6\left(nt\right)^{2}}{5w}$$

$$n\neq 0\text{ and }w\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 15wn^{2}, the least common multiple of 3n^{2},5w.

$$5w\times 2m=3n^{2}\times 4t^{2}$$

Multiply 5 and 2 to get 10.

$$10wm=3n^{2}\times 4t^{2}$$

Multiply 3 and 4 to get 12.

$$10wm=12n^{2}t^{2}$$

Divide both sides by 10w.

$$\frac{10wm}{10w}=\frac{12n^{2}t^{2}}{10w}$$

Dividing by 10w undoes the multiplication by 10w.

$$m=\frac{12n^{2}t^{2}}{10w}$$

Divide 12n^{2}t^{2} by 10w.

$$m=\frac{6n^{2}t^{2}}{5w}$$

Solve for n

$$\left\{\begin{matrix}n=\frac{\sqrt{30mw}}{6t}\text{; }n=-\frac{\sqrt{30mw}}{6t}\text{, }&\left(t\neq 0\text{ and }w<0\text{ and }m<0\right)\text{ or }\left(t\neq 0\text{ and }m>0\text{ and }w>0\right)\\n\neq 0\text{, }&t=0\text{ and }m=0\text{ and }w\neq 0\end{matrix}\right.$$