r^2f^2+8rf+12=

Solution for r^2f^2+8rf+12= equation:

Simplifying
r2f2 + 8rf + 12 = 0

Reorder the terms:
12 + 8fr + f2r2 = 0

Solving
12 + 8fr + f2r2 = 0

Solving for variable 'f'.

Factor a trinomial.
(6 + fr)(2 + fr) = 0

Subproblem 1
Set the factor '(6 + fr)' equal to zero and attempt to solve:

Simplifying
6 + fr = 0

Solving
6 + fr = 0

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

Add '-6' to each side of the equation.
6 + -6 + fr = 0 + -6

Combine like terms: 6 + -6 = 0
0 + fr = 0 + -6
fr = 0 + -6

Combine like terms: 0 + -6 = -6
fr = -6

Divide each side by 'r'.
f = -6r-1

Simplifying
f = -6r-1
Subproblem 2
Set the factor '(2 + fr)' equal to zero and attempt to solve:

Simplifying
2 + fr = 0

Solving
2 + fr = 0

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

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

Combine like terms: 2 + -2 = 0
0 + fr = 0 + -2
fr = 0 + -2

Combine like terms: 0 + -2 = -2
fr = -2

Divide each side by 'r'.
f = -2r-1

Simplifying
f = -2r-1
Solution
f = {-6r-1, -2r-1}