(n-3)(n-7)=0

Solution for (n-3)(n-7)=0 equation:

Simplifying
(n + -3)(n + -7) = 0

Reorder the terms:
(-3 + n)(n + -7) = 0

Reorder the terms:
(-3 + n)(-7 + n) = 0

Multiply (-3 + n) * (-7 + n)
(-3(-7 + n) + n(-7 + n)) = 0
((-7 * -3 + n * -3) + n(-7 + n)) = 0
((21 + -3n) + n(-7 + n)) = 0
(21 + -3n + (-7 * n + n * n)) = 0
(21 + -3n + (-7n + n2)) = 0

Combine like terms: -3n + -7n = -10n
(21 + -10n + n2) = 0

Solving
21 + -10n + n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(3 + -1n)(7 + -1n) = 0

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

Simplifying
3 + -1n = 0

Solving
3 + -1n = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1n = 0 + -3

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

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

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

Simplifying
n = 3
Subproblem 2
Set the factor '(7 + -1n)' equal to zero and attempt to solve:

Simplifying
7 + -1n = 0

Solving
7 + -1n = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1n = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1n = 0 + -7
-1n = 0 + -7

Combine like terms: 0 + -7 = -7
-1n = -7

Divide each side by '-1'.
n = 7

Simplifying
n = 7
Solution
n = {3, 7}