(f+4g)(f+2g)=

Solution for (f+4g)(f+2g)= equation:

Simplifying
(f + 4g)(f + 2g) = 0

Multiply (f + 4g) * (f + 2g)
(f(f + 2g) + 4g * (f + 2g)) = 0
((f * f + 2g * f) + 4g * (f + 2g)) = 0

Reorder the terms:
((2fg + f2) + 4g * (f + 2g)) = 0
((2fg + f2) + 4g * (f + 2g)) = 0
(2fg + f2 + (f * 4g + 2g * 4g)) = 0
(2fg + f2 + (4fg + 8g2)) = 0

Reorder the terms:
(2fg + 4fg + f2 + 8g2) = 0

Combine like terms: 2fg + 4fg = 6fg
(6fg + f2 + 8g2) = 0

Solving
6fg + f2 + 8g2 = 0

Solving for variable 'f'.

Factor a trinomial.
(f + 2g)(f + 4g) = 0

Subproblem 1
Set the factor '(f + 2g)' equal to zero and attempt to solve:

Simplifying
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
Subproblem 2
Set the factor '(f + 4g)' equal to zero and attempt to solve:

Simplifying
f + 4g = 0

Solving
f + 4g = 0

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

Add '-4g' to each side of the equation.
f + 4g + -4g = 0 + -4g

Combine like terms: 4g + -4g = 0
f + 0 = 0 + -4g
f = 0 + -4g
Remove the zero:
f = -4g

Simplifying
f = -4g
Solution
f = {-2g, -4g}