3fg(f+2g)=

Solution for 3fg(f+2g)= equation:

Simplifying
3fg(f + 2g) = 0
(f * 3fg + 2g * 3fg) = 0

Reorder the terms:
(6fg2 + 3f2g) = 0
(6fg2 + 3f2g) = 0

Solving
6fg2 + 3f2g = 0

Solving for variable 'f'.

Factor out the Greatest Common Factor (GCF), '3fg'.
3fg(2g + f) = 0

Ignore the factor 3.
Subproblem 1
Set the factor 'fg' equal to zero and attempt to solve:

Simplifying
fg = 0

Solving
fg = 0

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

Simplifying
fg = 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 '(2g + f)' equal to zero and attempt to solve:

Simplifying
2g + f = 0

Reorder the terms:
f + 2g = 0

Solving
f + 2g = 0

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

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

Combine like terms: 2g + -2g = 0
f + 0 = 0 + -2g
f = 0 + -2g
Remove the zero:
f = -2g

Simplifying
f = -2g
Solution
f = {-2g}