sin(x+pi)=-sin(x)

Solution for sin(x+pi)=-sin(x) equation:

Simplifying
sin(x + pi) = -1sin(x)

Reorder the terms:
ins(ip + x) = -1sin(x)
(ip * ins + x * ins) = -1sin(x)

Reorder the terms:
(insx + i2nps) = -1sin(x)
(insx + i2nps) = -1sin(x)

Multiply ins * x
insx + i2nps = -1insx

Solving
insx + i2nps = -1insx

Solving for variable 'i'.

Reorder the terms:
insx + insx + i2nps = -1insx + insx

Combine like terms: insx + insx = 2insx
2insx + i2nps = -1insx + insx

Combine like terms: -1insx + insx = 0
2insx + i2nps = 0

Factor out the Greatest Common Factor (GCF), 'ins'.
ins(2x + ip) = 0

Subproblem 1
Set the factor 'ins' equal to zero and attempt to solve:

Simplifying
ins = 0

Solving
ins = 0

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

Simplifying
ins = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(2x + ip)' equal to zero and attempt to solve:

Simplifying
2x + ip = 0

Reorder the terms:
ip + 2x = 0

Solving
ip + 2x = 0

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

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

Combine like terms: 2x + -2x = 0
ip + 0 = 0 + -2x
ip = 0 + -2x
Remove the zero:
ip = -2x

Divide each side by 'p'.
i = -2p-1x

Simplifying
i = -2p-1x
Solution
i = {-2p-1x}