Solve varepsilon^x+42s+xvarepsilon=k

$$\varepsilon ^ { x } + 42 s + x \varepsilon = k$$

Solve for s (complex solution)

$$s=\frac{k-\epsilon ^{x}-x\epsilon }{42}$$

Steps for Solving Linear Equation

Subtract \epsilon ^{x} from both sides.

$$42s+x\epsilon =k-\epsilon ^{x}$$

Subtract x\epsilon from both sides.

$$42s=k-\epsilon ^{x}-x\epsilon$$

Divide both sides by 42.

$$\frac{42s}{42}=\frac{k-\epsilon ^{x}-x\epsilon }{42}$$

Dividing by 42 undoes the multiplication by 42.

$$s=\frac{k-\epsilon ^{x}-x\epsilon }{42}$$

Solve for s

$$s=\frac{k-\epsilon ^{x}-x\epsilon }{42}$$

$$\left(\epsilon <0\text{ and }Denominator(x)\text{bmod}2=1\right)\text{ or }\left(\epsilon =0\text{ and }x>0\right)\text{ or }\epsilon >0$$

Steps for Solving Linear Equation

Subtract \epsilon ^{x} from both sides.

$$42s+x\epsilon =k-\epsilon ^{x}$$

Subtract x\epsilon from both sides.

$$42s=k-\epsilon ^{x}-x\epsilon$$

Divide both sides by 42.

$$\frac{42s}{42}=\frac{k-\epsilon ^{x}-x\epsilon }{42}$$

Dividing by 42 undoes the multiplication by 42.

$$s=\frac{k-\epsilon ^{x}-x\epsilon }{42}$$

Solve for k (complex solution)

$$k=x\epsilon +\epsilon ^{x}+42s$$

Solve for k

$$k=x\epsilon +\epsilon ^{x}+42s$$

$$\left(\epsilon <0\text{ and }Denominator(x)\text{bmod}2=1\right)\text{ or }\left(\epsilon =0\text{ and }x>0\right)\text{ or }\epsilon >0$$