(f+2)(f+7)=0

Solution for (f+2)(f+7)=0 equation:

Simplifying
(f + 2)(f + 7) = 0

Reorder the terms:
(2 + f)(f + 7) = 0

Reorder the terms:
(2 + f)(7 + f) = 0

Multiply (2 + f) * (7 + f)
(2(7 + f) + f(7 + f)) = 0
((7 * 2 + f * 2) + f(7 + f)) = 0
((14 + 2f) + f(7 + f)) = 0
(14 + 2f + (7 * f + f * f)) = 0
(14 + 2f + (7f + f2)) = 0

Combine like terms: 2f + 7f = 9f
(14 + 9f + f2) = 0

Solving
14 + 9f + f2 = 0

Solving for variable 'f'.

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

Subproblem 1
Set the factor '(7 + f)' equal to zero and attempt to solve:

Simplifying
7 + f = 0

Solving
7 + f = 0

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

Add '-7' to each side of the equation.
7 + -7 + f = 0 + -7

Combine like terms: 7 + -7 = 0
0 + f = 0 + -7
f = 0 + -7

Combine like terms: 0 + -7 = -7
f = -7

Simplifying
f = -7
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 = {-7, -2}