Solve A=35*10^-3-5*10^3+315*10^-2ct

$$A = 35 \times 10 ^ { - 3 } - 5 \times 10 ^ { 3 } + 315 \times 10 ^ { - 2 } ct$$

Solve for c (complex solution)

$$\left\{\begin{matrix}c=\frac{200A+999993}{630t}\text{, }&t\neq 0\\c\in \mathrm{C}\text{, }&A=-\frac{999993}{200}\text{ and }t=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Calculate 10 to the power of -3 and get \frac{1}{1000}.

$$A=35\times \frac{1}{1000}-5\times 10^{3}+315\times 10^{-2}ct$$

Multiply 35 and \frac{1}{1000} to get \frac{7}{200}.

$$A=\frac{7}{200}-5\times 10^{3}+315\times 10^{-2}ct$$

Calculate 10 to the power of 3 and get 1000.

$$A=\frac{7}{200}-5\times 1000+315\times 10^{-2}ct$$

Multiply 5 and 1000 to get 5000.

$$A=\frac{7}{200}-5000+315\times 10^{-2}ct$$

Subtract 5000 from \frac{7}{200} to get -\frac{999993}{200}.

$$A=-\frac{999993}{200}+315\times 10^{-2}ct$$

Calculate 10 to the power of -2 and get \frac{1}{100}.

$$A=-\frac{999993}{200}+315\times \frac{1}{100}ct$$

Multiply 315 and \frac{1}{100} to get \frac{63}{20}.

$$A=-\frac{999993}{200}+\frac{63}{20}ct$$

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

$$-\frac{999993}{200}+\frac{63}{20}ct=A$$

Add \frac{999993}{200} to both sides.

$$\frac{63}{20}ct=A+\frac{999993}{200}$$

The equation is in standard form.

$$\frac{63t}{20}c=A+\frac{999993}{200}$$

Divide both sides by \frac{63}{20}t.

$$\frac{20\times \frac{63t}{20}c}{63t}=\frac{20\left(A+\frac{999993}{200}\right)}{63t}$$

Dividing by \frac{63}{20}t undoes the multiplication by \frac{63}{20}t.

$$c=\frac{20\left(A+\frac{999993}{200}\right)}{63t}$$

Divide A+\frac{999993}{200} by \frac{63}{20}t.

$$c=\frac{200A+999993}{630t}$$

Solve for A

$$A=\frac{63ct}{20}-\frac{999993}{200}$$

Solution Steps

Calculate 10 to the power of -3 and get \frac{1}{1000}.

$$A=35\times \frac{1}{1000}-5\times 10^{3}+315\times 10^{-2}ct$$

Multiply 35 and \frac{1}{1000} to get \frac{7}{200}.

$$A=\frac{7}{200}-5\times 10^{3}+315\times 10^{-2}ct$$

Calculate 10 to the power of 3 and get 1000.

$$A=\frac{7}{200}-5\times 1000+315\times 10^{-2}ct$$

Multiply 5 and 1000 to get 5000.

$$A=\frac{7}{200}-5000+315\times 10^{-2}ct$$

Subtract 5000 from \frac{7}{200} to get -\frac{999993}{200}.

$$A=-\frac{999993}{200}+315\times 10^{-2}ct$$

Calculate 10 to the power of -2 and get \frac{1}{100}.

$$A=-\frac{999993}{200}+315\times \frac{1}{100}ct$$

Multiply 315 and \frac{1}{100} to get \frac{63}{20}.

$$A=-\frac{999993}{200}+\frac{63}{20}ct$$

Solve for c

$$\left\{\begin{matrix}c=\frac{200A+999993}{630t}\text{, }&t\neq 0\\c\in \mathrm{R}\text{, }&A=-\frac{999993}{200}\text{ and }t=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Calculate 10 to the power of -3 and get \frac{1}{1000}.

$$A=35\times \frac{1}{1000}-5\times 10^{3}+315\times 10^{-2}ct$$

Multiply 35 and \frac{1}{1000} to get \frac{7}{200}.

$$A=\frac{7}{200}-5\times 10^{3}+315\times 10^{-2}ct$$

Calculate 10 to the power of 3 and get 1000.

$$A=\frac{7}{200}-5\times 1000+315\times 10^{-2}ct$$

Multiply 5 and 1000 to get 5000.

$$A=\frac{7}{200}-5000+315\times 10^{-2}ct$$

Subtract 5000 from \frac{7}{200} to get -\frac{999993}{200}.

$$A=-\frac{999993}{200}+315\times 10^{-2}ct$$

Calculate 10 to the power of -2 and get \frac{1}{100}.

$$A=-\frac{999993}{200}+315\times \frac{1}{100}ct$$

Multiply 315 and \frac{1}{100} to get \frac{63}{20}.

$$A=-\frac{999993}{200}+\frac{63}{20}ct$$

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

$$-\frac{999993}{200}+\frac{63}{20}ct=A$$

Add \frac{999993}{200} to both sides.

$$\frac{63}{20}ct=A+\frac{999993}{200}$$

The equation is in standard form.

$$\frac{63t}{20}c=A+\frac{999993}{200}$$

Divide both sides by \frac{63}{20}t.

$$\frac{20\times \frac{63t}{20}c}{63t}=\frac{20\left(A+\frac{999993}{200}\right)}{63t}$$

Dividing by \frac{63}{20}t undoes the multiplication by \frac{63}{20}t.

$$c=\frac{20\left(A+\frac{999993}{200}\right)}{63t}$$

Divide A+\frac{999993}{200} by \frac{63}{20}t.

$$c=\frac{200A+999993}{630t}$$