cosx(cosx+5)=2cosx

Solution for cosx(cosx+5)=2cosx equation:

Simplifying
cosx(cosx + 5) = 2cosx

Reorder the terms:
cosx(5 + cosx) = 2cosx
(5 * cosx + cosx * cosx) = 2cosx
(5cosx + c2o2s2x2) = 2cosx

Solving
5cosx + c2o2s2x2 = 2cosx

Solving for variable 'c'.

Reorder the terms:
5cosx + -2cosx + c2o2s2x2 = 2cosx + -2cosx

Combine like terms: 5cosx + -2cosx = 3cosx
3cosx + c2o2s2x2 = 2cosx + -2cosx

Combine like terms: 2cosx + -2cosx = 0
3cosx + c2o2s2x2 = 0

Factor out the Greatest Common Factor (GCF), 'cosx'.
cosx(3 + cosx) = 0

Subproblem 1
Set the factor 'cosx' equal to zero and attempt to solve:

Simplifying
cosx = 0

Solving
cosx = 0

Move all terms containing c to the left, all other terms to the right.

Simplifying
cosx = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(3 + cosx)' equal to zero and attempt to solve:

Simplifying
3 + cosx = 0

Solving
3 + cosx = 0

Move all terms containing c to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + cosx = 0 + -3

Combine like terms: 3 + -3 = 0
0 + cosx = 0 + -3
cosx = 0 + -3

Combine like terms: 0 + -3 = -3
cosx = -3

Divide each side by 'osx'.
c = -3o-1s-1x-1

Simplifying
c = -3o-1s-1x-1
Solution
c = {-3o-1s-1x-1}