(2sinx+1)(2cosx+3)=0

Solution for (2sinx+1)(2cosx+3)=0 equation:

Simplifying
(2sinx + 1)(2cosx + 3) = 0

Reorder the terms:
(1 + 2insx)(2cosx + 3) = 0

Reorder the terms:
(1 + 2insx)(3 + 2cosx) = 0

Multiply (1 + 2insx) * (3 + 2cosx)
(1(3 + 2cosx) + 2insx * (3 + 2cosx)) = 0
((3 * 1 + 2cosx * 1) + 2insx * (3 + 2cosx)) = 0
((3 + 2cosx) + 2insx * (3 + 2cosx)) = 0
(3 + 2cosx + (3 * 2insx + 2cosx * 2insx)) = 0

Reorder the terms:
(3 + 2cosx + (4cinos2x2 + 6insx)) = 0
(3 + 2cosx + (4cinos2x2 + 6insx)) = 0

Reorder the terms:
(3 + 4cinos2x2 + 2cosx + 6insx) = 0
(3 + 4cinos2x2 + 2cosx + 6insx) = 0

Solving
3 + 4cinos2x2 + 2cosx + 6insx = 0

Solving for variable 'c'.

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

Add '-3' to each side of the equation.
3 + 4cinos2x2 + 2cosx + -3 + 6insx = 0 + -3

Reorder the terms:
3 + -3 + 4cinos2x2 + 2cosx + 6insx = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 4cinos2x2 + 2cosx + 6insx = 0 + -3
4cinos2x2 + 2cosx + 6insx = 0 + -3

Combine like terms: 0 + -3 = -3
4cinos2x2 + 2cosx + 6insx = -3

Add '-6insx' to each side of the equation.
4cinos2x2 + 2cosx + 6insx + -6insx = -3 + -6insx

Combine like terms: 6insx + -6insx = 0
4cinos2x2 + 2cosx + 0 = -3 + -6insx
4cinos2x2 + 2cosx = -3 + -6insx

Reorder the terms:
3 + 4cinos2x2 + 2cosx + 6insx = -3 + -6insx + 3 + 6insx

Reorder the terms:
3 + 4cinos2x2 + 2cosx + 6insx = -3 + 3 + -6insx + 6insx

Combine like terms: -3 + 3 = 0
3 + 4cinos2x2 + 2cosx + 6insx = 0 + -6insx + 6insx
3 + 4cinos2x2 + 2cosx + 6insx = -6insx + 6insx

Combine like terms: -6insx + 6insx = 0
3 + 4cinos2x2 + 2cosx + 6insx = 0

The solution to this equation could not be determined.