Sinx(Sinx+3)=-2

Solution for Sinx(Sinx+3)=-2 equation:

Simplifying
Sinx(Sinx + 3) = -2

Reorder the terms:
inxS(3 + inxS) = -2
(3 * inxS + inxS * inxS) = -2
(3inxS + i2n2x2S2) = -2

Solving
3inxS + i2n2x2S2 = -2

Solving for variable 'i'.

Reorder the terms:
2 + 3inxS + i2n2x2S2 = -2 + 2

Combine like terms: -2 + 2 = 0
2 + 3inxS + i2n2x2S2 = 0

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

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

Simplifying
2 + inxS = 0

Solving
2 + inxS = 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 + inxS = 0 + -2

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

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

Divide each side by 'nxS'.
i = -2n-1x-1S-1

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

Simplifying
1 + inxS = 0

Solving
1 + inxS = 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 + inxS = 0 + -1

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

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

Divide each side by 'nxS'.
i = -1n-1x-1S-1

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