F(x)=6x-2g(x)

Solution for F(x)=6x-2g(x) equation:

Simplifying
F(x) = 6x + -2g(x)

Multiply F * x
xF = 6x + -2g(x)

Multiply g * x
xF = 6x + -2gx

Reorder the terms:
xF = -2gx + 6x

Solving
xF = -2gx + 6x

Solving for variable 'x'.

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

Add '2gx' to each side of the equation.
2gx + xF = -2gx + 2gx + 6x

Combine like terms: -2gx + 2gx = 0
2gx + xF = 0 + 6x
2gx + xF = 6x

Add '-6x' to each side of the equation.
2gx + -6x + xF = 6x + -6x

Combine like terms: 6x + -6x = 0
2gx + -6x + xF = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(2g + -6 + 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 '(2g + -6 + F)' equal to zero and attempt to solve:

Simplifying
2g + -6 + F = 0

Reorder the terms:
-6 + F + 2g = 0

Solving
-6 + F + 2g = 0

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

Add '6' to each side of the equation.
-6 + F + 6 + 2g = 0 + 6

Reorder the terms:
-6 + 6 + F + 2g = 0 + 6

Combine like terms: -6 + 6 = 0
0 + F + 2g = 0 + 6
F + 2g = 0 + 6

Combine like terms: 0 + 6 = 6
F + 2g = 6

Add '-1F' to each side of the equation.
F + -1F + 2g = 6 + -1F

Combine like terms: F + -1F = 0
0 + 2g = 6 + -1F
2g = 6 + -1F

Add '-2g' to each side of the equation.
2g + -2g = 6 + -1F + -2g

Combine like terms: 2g + -2g = 0
0 = 6 + -1F + -2g

Simplifying
0 = 6 + -1F + -2g

The solution to this equation could not be determined.

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