(f-1)(f+3)=0

Solution for (f-1)(f+3)=0 equation:

Simplifying
(f + -1)(f + 3) = 0

Reorder the terms:
(-1 + f)(f + 3) = 0

Reorder the terms:
(-1 + f)(3 + f) = 0

Multiply (-1 + f) * (3 + f)
(-1(3 + f) + f(3 + f)) = 0
((3 * -1 + f * -1) + f(3 + f)) = 0
((-3 + -1f) + f(3 + f)) = 0
(-3 + -1f + (3 * f + f * f)) = 0
(-3 + -1f + (3f + f2)) = 0

Combine like terms: -1f + 3f = 2f
(-3 + 2f + f2) = 0

Solving
-3 + 2f + f2 = 0

Solving for variable 'f'.

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

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 '(1 + -1f)' equal to zero and attempt to solve:

Simplifying
1 + -1f = 0

Solving
1 + -1f = 0

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

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

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

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

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

Simplifying
f = 1
Solution
f = {-3, 1}