(4-n)(6-n)=0

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

Simplifying
(4 + -1n)(6 + -1n) = 0

Multiply (4 + -1n) * (6 + -1n)
(4(6 + -1n) + -1n * (6 + -1n)) = 0
((6 * 4 + -1n * 4) + -1n * (6 + -1n)) = 0
((24 + -4n) + -1n * (6 + -1n)) = 0
(24 + -4n + (6 * -1n + -1n * -1n)) = 0
(24 + -4n + (-6n + 1n2)) = 0

Combine like terms: -4n + -6n = -10n
(24 + -10n + 1n2) = 0

Solving
24 + -10n + 1n2 = 0

Solving for variable 'n'.

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

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

Simplifying
4 + -1n = 0

Solving
4 + -1n = 0

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

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

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

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

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

Simplifying
n = 4
Subproblem 2
Set the factor '(6 + -1n)' equal to zero and attempt to solve:

Simplifying
6 + -1n = 0

Solving
6 + -1n = 0

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

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

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

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

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

Simplifying
n = 6
Solution
n = {4, 6}