Solve 0=2.1m+(4.5831m/s)t-1/2(9.81m/s^2)t^2

$$0 = 2.1 m + ( 4.5831 m / s ) t - \frac { 1 } { 2 } ( 9.81 m / s ^ { 2 } ) t ^ { 2 }$$

Solve for m

$$\left\{\begin{matrix}\\m=0\text{, }&\text{unconditionally}\\m\in \mathrm{R}\text{, }&\left(s=\frac{\sqrt{691186729}t-15277t}{14000}\text{ or }s=\frac{-\sqrt{691186729}t-15277t}{14000}\right)\text{ and }t\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2s^{2}, the least common multiple of s,2,s^{2}.

$$0=2s^{2}\left(2.1m+\frac{4.5831m}{s}t\right)-\frac{1}{2}\times 2\times 9.81mt^{2}$$

Use the distributive property to multiply 2s^{2} by 2.1m+\frac{4.5831m}{s}t.

$$0=4.2s^{2}m+2s^{2}\times \frac{4.5831m}{s}t-\frac{1}{2}\times 2\times 9.81mt^{2}$$

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

$$0=4.2s^{2}m+2s^{2}\times \frac{4.5831m}{s}t-9.81mt^{2}$$

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

$$4.2s^{2}m+2s^{2}\times \frac{4.5831m}{s}t-9.81mt^{2}=0$$

Multiply both sides of the equation by s.

$$s\left(4.2s^{2}m+2s^{2}\times \frac{4.5831m}{s}t\right)-9.81mt^{2}s=0$$

Multiply both sides of the equation by s.

$$s\left(4.2s^{2}m+2s^{2}\times \frac{4.5831m}{s}t\right)s-9.81mt^{2}ss=0$$

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

$$s^{2}\left(4.2s^{2}m+2s^{2}\times \frac{4.5831m}{s}t\right)-9.81mt^{2}ss=0$$

Use the distributive property to multiply s^{2} by 4.2s^{2}m+2s^{2}\times \frac{4.5831m}{s}t.

$$4.2ms^{4}+2\times \frac{4.5831m}{s}ts^{4}-9.81mt^{2}ss=0$$

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

$$4.2ms^{4}+2\times \frac{4.5831m}{s}ts^{4}-9.81mt^{2}s^{2}=0$$

Multiply both sides of the equation by s.

$$4.2ms^{4}s+2\times 4.5831mts^{4}-9.81mt^{2}s^{2}s=0$$

Reorder the terms.

$$4.2mss^{4}-9.81mss^{2}t^{2}+2\times 4.5831mts^{4}=0$$

To multiply powers of the same base, add their exponents. Add 1 and 4 to get 5.

$$4.2ms^{5}-9.81mss^{2}t^{2}+2\times 4.5831mts^{4}=0$$

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

$$4.2ms^{5}-9.81ms^{3}t^{2}+2\times 4.5831mts^{4}=0$$

Multiply 2 and 4.5831 to get 9.1662.

$$4.2ms^{5}-9.81ms^{3}t^{2}+9.1662mts^{4}=0$$

Combine all terms containing m.

$$\left(4.2s^{5}-9.81s^{3}t^{2}+9.1662ts^{4}\right)m=0$$

The equation is in standard form.

$$\left(-\frac{981t^{2}s^{3}}{100}+\frac{45831ts^{4}}{5000}+\frac{21s^{5}}{5}\right)m=0$$

Divide 0 by 4.2s^{5}-9.81s^{3}t^{2}+9.1662ts^{4}.

$$m=0$$

Solve for s

$$\left\{\begin{matrix}\\s\neq 0\text{, }&\text{unconditionally}\\s=\frac{\left(\sqrt{691186729}-15277\right)t}{14000}\text{; }s=-\frac{\left(\sqrt{691186729}+15277\right)t}{14000}\text{, }&t\neq 0\end{matrix}\right.$$