n^2-28n+75=0

Solution for n^2-28n+75=0 equation:

Simplifying
n2 + -28n + 75 = 0

Reorder the terms:
75 + -28n + n2 = 0

Solving
75 + -28n + n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(3 + -1n)(25 + -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 '(25 + -1n)' equal to zero and attempt to solve:

Simplifying
25 + -1n = 0

Solving
25 + -1n = 0

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

Add '-25' to each side of the equation.
25 + -25 + -1n = 0 + -25

Combine like terms: 25 + -25 = 0
0 + -1n = 0 + -25
-1n = 0 + -25

Combine like terms: 0 + -25 = -25
-1n = -25

Divide each side by '-1'.
n = 25

Simplifying
n = 25
Solution
n = {3, 25}