(3f+9)(f-5)=0

Solution for (3f+9)(f-5)=0 equation:

Simplifying
(3f + 9)(f + -5) = 0

Reorder the terms:
(9 + 3f)(f + -5) = 0

Reorder the terms:
(9 + 3f)(-5 + f) = 0

Multiply (9 + 3f) * (-5 + f)
(9(-5 + f) + 3f * (-5 + f)) = 0
((-5 * 9 + f * 9) + 3f * (-5 + f)) = 0
((-45 + 9f) + 3f * (-5 + f)) = 0
(-45 + 9f + (-5 * 3f + f * 3f)) = 0
(-45 + 9f + (-15f + 3f2)) = 0

Combine like terms: 9f + -15f = -6f
(-45 + -6f + 3f2) = 0

Solving
-45 + -6f + 3f2 = 0

Solving for variable 'f'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-15 + -2f + f2) = 0

Factor a trinomial.
3((-3 + -1f)(5 + -1f)) = 0

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

Simplifying
-3 + -1f = 0

Solving
-3 + -1f = 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 + -1f = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1f = 0 + 3
-1f = 0 + 3

Combine like terms: 0 + 3 = 3
-1f = 3

Divide each side by '-1'.
f = -3

Simplifying
f = -3
Subproblem 2
Set the factor '(5 + -1f)' equal to zero and attempt to solve:

Simplifying
5 + -1f = 0

Solving
5 + -1f = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1f = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1f = 0 + -5
-1f = 0 + -5

Combine like terms: 0 + -5 = -5
-1f = -5

Divide each side by '-1'.
f = 5

Simplifying
f = 5
Solution
f = {-3, 5}