(n-7)(n-5)=0

Solution for (n-7)(n-5)=0 equation:

Simplifying
(n + -7)(n + -5) = 0

Reorder the terms:
(-7 + n)(n + -5) = 0

Reorder the terms:
(-7 + n)(-5 + n) = 0

Multiply (-7 + n) * (-5 + n)
(-7(-5 + n) + n(-5 + n)) = 0
((-5 * -7 + n * -7) + n(-5 + n)) = 0
((35 + -7n) + n(-5 + n)) = 0
(35 + -7n + (-5 * n + n * n)) = 0
(35 + -7n + (-5n + n2)) = 0

Combine like terms: -7n + -5n = -12n
(35 + -12n + n2) = 0

Solving
35 + -12n + n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(5 + -1n)(7 + -1n) = 0

Subproblem 1
Set the factor '(5 + -1n)' equal to zero and attempt to solve:

Simplifying
5 + -1n = 0

Solving
5 + -1n = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1n = 0 + -5
-1n = 0 + -5

Combine like terms: 0 + -5 = -5
-1n = -5

Divide each side by '-1'.
n = 5

Simplifying
n = 5
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 = {5, 7}