cosx(2cosx+5)=-2

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

Simplifying
cosx(2cosx + 5) = -2

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

Solving
5cosx + 2c2o2s2x2 = -2

Solving for variable 'c'.

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

Combine like terms: -2 + 2 = 0
2 + 5cosx + 2c2o2s2x2 = 0

Factor a trinomial.
(2 + cosx)(1 + 2cosx) = 0

Subproblem 1
Set the factor '(2 + cosx)' equal to zero and attempt to solve:

Simplifying
2 + cosx = 0

Solving
2 + cosx = 0

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

Add '-2' to each side of the equation.
2 + -2 + cosx = 0 + -2

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

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

Divide each side by 'osx'.
c = -2o-1s-1x-1

Simplifying
c = -2o-1s-1x-1
Subproblem 2
Set the factor '(1 + 2cosx)' equal to zero and attempt to solve:

Simplifying
1 + 2cosx = 0

Solving
1 + 2cosx = 0

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

Add '-1' to each side of the equation.
1 + -1 + 2cosx = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2cosx = 0 + -1
2cosx = 0 + -1

Combine like terms: 0 + -1 = -1
2cosx = -1

Divide each side by '2osx'.
c = -0.5o-1s-1x-1

Simplifying
c = -0.5o-1s-1x-1
Solution
c = {-2o-1s-1x-1, -0.5o-1s-1x-1}