(f+9)(f+2)=0

Solution for (f+9)(f+2)=0 equation:

Simplifying
(f + 9)(f + 2) = 0

Reorder the terms:
(9 + f)(f + 2) = 0

Reorder the terms:
(9 + f)(2 + f) = 0

Multiply (9 + f) * (2 + f)
(9(2 + f) + f(2 + f)) = 0
((2 * 9 + f * 9) + f(2 + f)) = 0
((18 + 9f) + f(2 + f)) = 0
(18 + 9f + (2 * f + f * f)) = 0
(18 + 9f + (2f + f2)) = 0

Combine like terms: 9f + 2f = 11f
(18 + 11f + f2) = 0

Solving
18 + 11f + f2 = 0

Solving for variable 'f'.

Factor a trinomial.
(9 + f)(2 + f) = 0

Subproblem 1
Set the factor '(9 + f)' equal to zero and attempt to solve:

Simplifying
9 + f = 0

Solving
9 + f = 0

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

Add '-9' to each side of the equation.
9 + -9 + f = 0 + -9

Combine like terms: 9 + -9 = 0
0 + f = 0 + -9
f = 0 + -9

Combine like terms: 0 + -9 = -9
f = -9

Simplifying
f = -9
Subproblem 2
Set the factor '(2 + f)' equal to zero and attempt to solve:

Simplifying
2 + f = 0

Solving
2 + f = 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 + f = 0 + -2

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

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

Simplifying
f = -2
Solution
f = {-9, -2}