F(x)=x+sinx

Solution for F(x)=x+sinx equation:

Simplifying
F(x) = x + sinx

Multiply F * x
xF = x + sinx

Reorder the terms:
xF = insx + x

Solving
xF = insx + x

Solving for variable 'x'.

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

Add '-1insx' to each side of the equation.
-1insx + xF = insx + -1insx + x

Combine like terms: insx + -1insx = 0
-1insx + xF = 0 + x
-1insx + xF = x

Add '-1x' to each side of the equation.
-1insx + -1x + xF = x + -1x

Combine like terms: x + -1x = 0
-1insx + -1x + xF = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-1ins + -1 + F) = 0

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

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(-1ins + -1 + F)' equal to zero and attempt to solve:

Simplifying
-1ins + -1 + F = 0

Reorder the terms:
-1 + F + -1ins = 0

Solving
-1 + F + -1ins = 0

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

Add '1' to each side of the equation.
-1 + F + 1 + -1ins = 0 + 1

Reorder the terms:
-1 + 1 + F + -1ins = 0 + 1

Combine like terms: -1 + 1 = 0
0 + F + -1ins = 0 + 1
F + -1ins = 0 + 1

Combine like terms: 0 + 1 = 1
F + -1ins = 1

Add '-1F' to each side of the equation.
F + -1F + -1ins = 1 + -1F

Combine like terms: F + -1F = 0
0 + -1ins = 1 + -1F
-1ins = 1 + -1F

Add 'ins' to each side of the equation.
-1ins + ins = 1 + -1F + ins

Combine like terms: -1ins + ins = 0
0 = 1 + -1F + ins

Simplifying
0 = 1 + -1F + ins

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}