Solve -5θ=ecθ+7/cosθ

$$- 5 \theta = e c \theta + \frac { 7 } { \cos \theta }$$

Solve for c

$$c=\frac{-5\theta \cos(\theta )-7}{e\theta \cos(\theta )}$$

$$\theta \neq 0\text{ and }\nexists n_{1}\in \mathrm{Z}\text{ : }\theta =\pi n_{1}+\frac{\pi }{2}$$

Steps for Solving Linear Equation

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

$$ec\theta +\frac{7}{\cos(\theta )}=-5\theta$$

Subtract \frac{7}{\cos(\theta )} from both sides.

$$ec\theta =-5\theta -\frac{7}{\cos(\theta )}$$

The equation is in standard form.

$$e\theta c=-\frac{7}{\cos(\theta )}-5\theta$$

Divide both sides by e\theta .

$$\frac{e\theta c}{e\theta }=\frac{-\frac{7}{\cos(\theta )}-5\theta }{e\theta }$$

Dividing by e\theta undoes the multiplication by e\theta .

$$c=\frac{-\frac{7}{\cos(\theta )}-5\theta }{e\theta }$$

Divide -\frac{7}{\cos(\theta )}-5\theta by e\theta .

$$c=-\frac{\frac{7}{\theta \cos(\theta )}+5}{e}$$