f^2+6=-5f

Solution for f^2+6=-5f equation:

Simplifying
f2 + 6 = -5f

Reorder the terms:
6 + f2 = -5f

Solving
6 + f2 = -5f

Solving for variable 'f'.

Reorder the terms:
6 + 5f + f2 = -5f + 5f

Combine like terms: -5f + 5f = 0
6 + 5f + f2 = 0

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

Subproblem 1
Set the factor '(3 + f)' equal to zero and attempt to solve:

Simplifying
3 + f = 0

Solving
3 + f = 0

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

Add '-3' to each side of the equation.
3 + -3 + f = 0 + -3

Combine like terms: 3 + -3 = 0
0 + f = 0 + -3
f = 0 + -3

Combine like terms: 0 + -3 = -3
f = -3

Simplifying
f = -3
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 = {-3, -2}