4cos(x)(cos(x)+1)-3=0

Solution for 4cos(x)(cos(x)+1)-3=0 equation:

Simplifying
4cos(x)(cos(x) + 1) + -3 = 0

Multiply cos * x
4cos * x(cosx + 1) + -3 = 0

Reorder the terms:
4cos * x(1 + cosx) + -3 = 0

Multiply cos * x
4cosx(1 + cosx) + -3 = 0
(1 * 4cosx + cosx * 4cosx) + -3 = 0
(4cosx + 4c2o2s2x2) + -3 = 0

Reorder the terms:
-3 + 4cosx + 4c2o2s2x2 = 0

Solving
-3 + 4cosx + 4c2o2s2x2 = 0

Solving for variable 'c'.

Factor a trinomial.
(-3 + -2cosx)(1 + -2cosx) = 0

Subproblem 1
Set the factor '(-3 + -2cosx)' equal to zero and attempt to solve:

Simplifying
-3 + -2cosx = 0

Solving
-3 + -2cosx = 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 + -2cosx = 0 + 3

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

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

Divide each side by '-2osx'.
c = -1.5o-1s-1x-1

Simplifying
c = -1.5o-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 = {-1.5o-1s-1x-1, 0.5o-1s-1x-1}