cosx(2cosx+1)=1

Solution for cosx(2cosx+1)=1 equation:

Simplifying
cosx(2cosx + 1) = 1

Reorder the terms:
cosx(1 + 2cosx) = 1
(1 * cosx + 2cosx * cosx) = 1
(1cosx + 2c2o2s2x2) = 1

Solving
1cosx + 2c2o2s2x2 = 1

Solving for variable 'c'.

Reorder the terms:
-1 + 1cosx + 2c2o2s2x2 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + 1cosx + 2c2o2s2x2 = 0

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

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

Simplifying
-1 + -1cosx = 0

Solving
-1 + -1cosx = 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 + -1cosx = 0 + 1

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

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

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

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