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

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

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

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

Multiply (1 + 2insx) * (2 + insx)
(1(2 + insx) + 2insx * (2 + insx)) = 0
((2 * 1 + insx * 1) + 2insx * (2 + insx)) = 0
((2 + 1insx) + 2insx * (2 + insx)) = 0
(2 + 1insx + (2 * 2insx + insx * 2insx)) = 0
(2 + 1insx + (4insx + 2i2n2s2x2)) = 0

Combine like terms: 1insx + 4insx = 5insx
(2 + 5insx + 2i2n2s2x2) = 0

Solving
2 + 5insx + 2i2n2s2x2 = 0

Solving for variable 'i'.

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

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

Simplifying
2 + insx = 0

Solving
2 + insx = 0

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

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

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

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

Divide each side by 'nsx'.
i = -2n-1s-1x-1

Simplifying
i = -2n-1s-1x-1
Subproblem 2
Set the factor '(1 + 2insx)' equal to zero and attempt to solve:

Simplifying
1 + 2insx = 0

Solving
1 + 2insx = 0

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

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

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

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

Divide each side by '2nsx'.
i = -0.5n-1s-1x-1

Simplifying
i = -0.5n-1s-1x-1
Solution
i = {-2n-1s-1x-1, -0.5n-1s-1x-1}