(f-6)(f-4)=0

Solution for (f-6)(f-4)=0 equation:

Simplifying
(f + -6)(f + -4) = 0

Reorder the terms:
(-6 + f)(f + -4) = 0

Reorder the terms:
(-6 + f)(-4 + f) = 0

Multiply (-6 + f) * (-4 + f)
(-6(-4 + f) + f(-4 + f)) = 0
((-4 * -6 + f * -6) + f(-4 + f)) = 0
((24 + -6f) + f(-4 + f)) = 0
(24 + -6f + (-4 * f + f * f)) = 0
(24 + -6f + (-4f + f2)) = 0

Combine like terms: -6f + -4f = -10f
(24 + -10f + f2) = 0

Solving
24 + -10f + f2 = 0

Solving for variable 'f'.

Factor a trinomial.
(4 + -1f)(6 + -1f) = 0

Subproblem 1
Set the factor '(4 + -1f)' equal to zero and attempt to solve:

Simplifying
4 + -1f = 0

Solving
4 + -1f = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1f = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1f = 0 + -4
-1f = 0 + -4

Combine like terms: 0 + -4 = -4
-1f = -4

Divide each side by '-1'.
f = 4

Simplifying
f = 4
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 = {4, 6}