F(x)=Tgx-x

Solution for F(x)=Tgx-x equation:

Simplifying
F(x) = Tgx + -1x

Multiply F * x
xF = Tgx + -1x

Solving
xF = gxT + -1x

Solving for variable 'x'.

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

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

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

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

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

Factor out the Greatest Common Factor (GCF), 'x'.
x(-1gT + 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 '(-1gT + 1 + F)' equal to zero and attempt to solve:

Simplifying
-1gT + 1 + F = 0

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

Solving
1 + F + -1gT = 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 + -1gT = 0 + -1

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

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

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

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

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

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

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

Simplifying
0 = -1 + -1F + gT

The solution to this equation could not be determined.

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