(f-6)(f-3)=0

Solution for (f-6)(f-3)=0 equation:

Simplifying
(f + -6)(f + -3) = 0

Reorder the terms:
(-6 + f)(f + -3) = 0

Reorder the terms:
(-6 + f)(-3 + f) = 0

Multiply (-6 + f) * (-3 + f)
(-6(-3 + f) + f(-3 + f)) = 0
((-3 * -6 + f * -6) + f(-3 + f)) = 0
((18 + -6f) + f(-3 + f)) = 0
(18 + -6f + (-3 * f + f * f)) = 0
(18 + -6f + (-3f + f2)) = 0

Combine like terms: -6f + -3f = -9f
(18 + -9f + f2) = 0

Solving
18 + -9f + f2 = 0

Solving for variable 'f'.

Factor a trinomial.
(3 + -1f)(6 + -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 '(6 + -1f)' equal to zero and attempt to solve:

Simplifying
6 + -1f = 0

Solving
6 + -1f = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1f = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1f = 0 + -6
-1f = 0 + -6

Combine like terms: 0 + -6 = -6
-1f = -6

Divide each side by '-1'.
f = 6

Simplifying
f = 6
Solution
f = {3, 6}