Solve 23/7kquad123hbar+287k=40

$$\frac { 23 } { 7 } k \quad 123 \hbar + 287 k = 40$$

Solve for k_123 (complex solution)

$$\left\{\begin{matrix}k_{123}=-\frac{7\left(287k-40\right)}{23ℏ}\text{, }&ℏ\neq 0\\k_{123}\in \mathrm{C}\text{, }&k=\frac{40}{287}\text{ and }ℏ=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 287k from both sides.

$$\frac{23}{7}k_{123}ℏ=40-287k$$

The equation is in standard form.

$$\frac{23ℏ}{7}k_{123}=40-287k$$

Divide both sides by \frac{23}{7}ℏ.

$$\frac{7\times \frac{23ℏ}{7}k_{123}}{23ℏ}=\frac{7\left(40-287k\right)}{23ℏ}$$

Dividing by \frac{23}{7}ℏ undoes the multiplication by \frac{23}{7}ℏ.

$$k_{123}=\frac{7\left(40-287k\right)}{23ℏ}$$

Solve for k

$$k=-\frac{23k_{123}ℏ}{2009}+\frac{40}{287}$$

Steps for Solving Linear Equation

Subtract \frac{23}{7}k_{123}ℏ from both sides.

$$287k=40-\frac{23}{7}k_{123}ℏ$$

The equation is in standard form.

$$287k=-\frac{23k_{123}ℏ}{7}+40$$

Divide both sides by 287.

$$\frac{287k}{287}=\frac{-\frac{23k_{123}ℏ}{7}+40}{287}$$

Dividing by 287 undoes the multiplication by 287.

$$k=\frac{-\frac{23k_{123}ℏ}{7}+40}{287}$$

Divide 40-\frac{23k_{123}ℏ}{7} by 287.

$$k=-\frac{23k_{123}ℏ}{2009}+\frac{40}{287}$$

Solve for k_123

$$\left\{\begin{matrix}k_{123}=-\frac{7\left(287k-40\right)}{23ℏ}\text{, }&ℏ\neq 0\\k_{123}\in \mathrm{R}\text{, }&k=\frac{40}{287}\text{ and }ℏ=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 287k from both sides.

$$\frac{23}{7}k_{123}ℏ=40-287k$$

The equation is in standard form.

$$\frac{23ℏ}{7}k_{123}=40-287k$$

Divide both sides by \frac{23}{7}ℏ.

$$\frac{7\times \frac{23ℏ}{7}k_{123}}{23ℏ}=\frac{7\left(40-287k\right)}{23ℏ}$$

Dividing by \frac{23}{7}ℏ undoes the multiplication by \frac{23}{7}ℏ.

$$k_{123}=\frac{7\left(40-287k\right)}{23ℏ}$$