Solve 5*m=1/2g*(5s)^2

$$5 \times m = \frac { 1 } { 2 } g \times ( 5 s ) ^ { 2 }$$

Solve for g

$$\left\{\begin{matrix}g=\frac{2m}{5s^{2}}\text{, }&s\neq 0\\g\in \mathrm{R}\text{, }&m=0\text{ and }s=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Expand \left(5s\right)^{2}.

$$5m=\frac{1}{2}g\times 5^{2}s^{2}$$

Calculate 5 to the power of 2 and get 25.

$$5m=\frac{1}{2}g\times 25s^{2}$$

Multiply \frac{1}{2} and 25 to get \frac{25}{2}.

$$5m=\frac{25}{2}gs^{2}$$

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

$$\frac{25}{2}gs^{2}=5m$$

The equation is in standard form.

$$\frac{25s^{2}}{2}g=5m$$

Divide both sides by \frac{25}{2}s^{2}.

$$\frac{2\times \frac{25s^{2}}{2}g}{25s^{2}}=\frac{2\times 5m}{25s^{2}}$$

Dividing by \frac{25}{2}s^{2} undoes the multiplication by \frac{25}{2}s^{2}.

$$g=\frac{2\times 5m}{25s^{2}}$$

Divide 5m by \frac{25}{2}s^{2}.

$$g=\frac{2m}{5s^{2}}$$

Solve for m

$$m=\frac{5gs^{2}}{2}$$

Steps for Solving Linear Equation

Expand \left(5s\right)^{2}.

$$5m=\frac{1}{2}g\times 5^{2}s^{2}$$

Calculate 5 to the power of 2 and get 25.

$$5m=\frac{1}{2}g\times 25s^{2}$$

Multiply \frac{1}{2} and 25 to get \frac{25}{2}.

$$5m=\frac{25}{2}gs^{2}$$

The equation is in standard form.

$$5m=\frac{25gs^{2}}{2}$$

Divide both sides by 5.

$$\frac{5m}{5}=\frac{25gs^{2}}{2\times 5}$$

Dividing by 5 undoes the multiplication by 5.

$$m=\frac{25gs^{2}}{2\times 5}$$

Divide \frac{25gs^{2}}{2} by 5.

$$m=\frac{5gs^{2}}{2}$$